I needed to make notes on all the abilities for my mod to get the balance right. It's not as nicely laid out as the OP or that spreadsheet, but it has most of the information from v1.52 of Rebellion, and is better than nothing. The only ship I didn't get round to writing up was the Rankulas because it creates ships and was hard to summarise.
TEC (Kol Battleship)
Gauss Rail Gun: Fire at hostile non-strikecraft within 6500 km for 400/670/940/1210 dmg, slowing movement by -100% for 10sec. (50/55/60/65AM, 6sec)
Flak Burst: Deal 30/43/56/69 dmg to hostile strikecraft within 3000/3380/3760/4140 km. (100AM, 12/10/8/7sec)
Adaptive Forcefield: Reduce damage taken by 15/23/32/40% and phase missile penetration by 24/42/58/75% for 20/29/37/46sec. (40/50/60/70AM, 45/40/35/30sec)
Finest Hour: Kol repairs 15/18.75 hull per sec, restores 3/3.75 antimatter per sec, reduces ability cooldowns by 20/25%, and gains 60/75 splash damage (1000 radius) on attacks for 60 sec. (150AM, 180sec)
TEC (Sova Carrier)
Missile Batteries: Deploy missile turret for 180 sec, with 13.0/17.52/23.2/30.78 dps, 750/979/1208/1438 hull, 120/140/160/185 shield, 3/4/5/6 armor. (70AM, 35sec)
Embargo: Disable trade ship phase jump engines, increases ship & structure build time in current system by 30%/53%/77%/100%, and steals 40/60/80/100% of planet/income production for 60/86/112/138 sec. (85AM, 120sec)
Heavy Fighters: (Passive) Increases this Sova's strikecraft's armor by 2/3.25/4.5/5.75 and damage dealt by 12%/22%/32%/41%.
Rapid Manufacturing: For 90/113 sec, this Sova's replacement strikecraft are built instantly, and ship & structure build time in current system is reduced by 250%. (120/90AM, 180/135sec)
TEC (Akkan Battlecruiser)
Colonize+: Colonize target planet within 5000 km, automatically build 1/2/3/3 free extractors in current system, and increase extraction rate by 33/55/78/100%. (90AM, 120/97/74/51sec)
Ion Bolt: Interrupt and completely disable target hostile non-titan/strikecraft within 7000 km for 3/5/6/8 sec. (85AM, 10/12/14/16sec)
Targeting Uplink: (Passive) Increase weapon range by 8%/15%/22%/29% and accuracy by 5%/9%/13%/17% for friendly non-strikecraft within 8000 km.
Armistice: All ships and structures within 12000 km have their weapons & abilities disabled and are invulnerable for 60/75 sec. (150/113AM, 180sec)
TEC (Dunov Battlecruiser)
Shield Restore: Instantly regenerate 250/455/660/865 shield of target friendly within 6000 km. Dunov cannot target self, and target must not be at full shields. (65AM, 11sec)
EMP Charge: Deal 150/275/395/520 dmg to and remove 50/91/132/173 antimatter from target hostile non-strikecraft within 4500/5110/5720/6325 km, and all hostile non-strikecraft within 2500/3010/3515/4025 km of target. (90AM, 40/35/30/25sec)
Magnetize: Disable target hostile non-titan/strikecraft's abilities for 10/12/15/17 sec (or after 12/19/25/32 strikecraft killed) and causes 8/11/15/18 hostile strikecraft/corvettes within 5000/6020/7035/8050 km to collide with it, dealing 25 dmg per impact. (80AM, 15sec)
Flux Field: Reduce antimatter cost of abilities by 300%/345% for friendlies within 4000 km, for 60/75 sec. (125/95AM, 180/135sec)
TEC (Marza Dreadnought)
Radiation Bomb: Deal 125/227/329/431 to target hostile non-corvette/strikecraft within 6000 km. Target and hostile non-strikecraft within 1200 km of it receive 7/13/18/24 dmg per sec for 4 sec. (85AM, 12sec)
Raze Planet: Target hostile planet within 5000 km is dealt 160/320/400/560 dmg and has 20/40/50/70 population killed. (90/80/70/60AM, 40/45/50/55sec)
Incendiary Shells: (Passive) This Marza's weapons do an extra 3/4.3/5.6/6.9 dmg per sec for 15 sec to targets it successfully hits.
Missile Barrage: Deal 120/150 x25 (3000/3750) dmg to all objects in target area within 8000km. (150/112AM, 240/180sec)
TEC (Corsev Battlecruiser)
Boarding Party: Deals 35/40/45/50 damage per second to targetted enemy frigate/module for 10/13/17/20 secs. If target would have died, it is instead healed 50% hull and 100% shields and converted to your side. (100/95/90/85AM, 60sec)
Demolition Team: Destroys targeted friendly frigate/module within 8000 km, dealing 300/433/567/700 damage (600/866/1133/1400 if target was boarded) to up to 25 enemies within 2000/2500/3000/3500 (if target was boarded, 2500/3000/3500/4000 range). (85AM, 90/80/70/60sec)
Salvage Operations: (Passive) Whenever friendly ship dies within 4000/4500/5000/5500 range, gain 15%/20%/25%/30% of the ship's max hull points (20%/25%/30%/35% hull points if destroyed ship was boarded).
Elite Crews: Target friendly capital ship within 5000 range gains 33%/66% damage, 70%/100% shield restore rate, and 25%/50% speed/acceleration for 180/240sec. (90AM, 70sec)
Advent (Radiance Battleship)
Detonate Antimatter: Disable antimatter abilities of hostile non-corvette/strikecraft within 4500 km, draining 10 AM per second and doing 12/14/17/20 dmg per sec to them for 12/15/18/21 sec. (60AM, 20sec)
Animosity: Force 8/18/27/37 hostile non-strikecraft within 3000/3920/4835/5750 km to attack this ship for 20 secs. (65AM, 35sec)
Energy Absorptive Armor: (Passive) Turn 5%/9%/13%/17% of dmg received to Antimatter, increase Armor by 2/3.6/5.27/6.9.
Cleansing Brilliance: Fire at target hostile non-corvette/strikecraft within 8000/10000 km and do 250/312 (2000/2496) dmg over 8 sec to target and hostiles it passes through (1000/1250 beam width). (150AM, 120sec)
Advent (Halcyon Carrier)
Telekinetic Push: Push away hostile strikecraft within 4200 range, dealing 20/28.6/37.3/46 dmg and reducing their max speed & acceleration by 25%/45%/66%/86%. (90AM, 10sec)
Adept Drone Anima: (Passive) Increase number of strikecraft squadrons by 1/2/3/4 for this Halcyon.
Amplify Energy Aura: (Passive) Reduces energy weapon cooldown by 8%/14%/20%/26% for all friendlies within 8000 range.
Anima Tempest: Instantly create 60/75 temporary strikecraft for 75/95 sec, which are divided among existing squadrons, or form a new squadron if none exist. Also increases chance to hit on all linked strike craft by 25/31% (150/110AM, 180sec)
Advent (Progenitor Mothership)
Colonize: Colonize target planet within 5000 km and reduces Develop Planet cost by 15%/27%/40%/52% for 360/470/580/690 sec. (90AM, 120/90/60sec)
Malice: Target hostile non-strikecraft within 8000 km, and 8/15/21/28 hostile non-strikecraft within 3000 km target, share 30% dmg whenever one of them takes dmg, for 10 sec. (50AM, 10sec)
Shield Regeneration: Regen 37.5/49/60.5/72 shield per sec for 8 sec on self and friendlies within 3000/3533/4067/4600 range. (100AM, 20sec)
Resurrection: Transfer dead Capital's Ship lvl to new Capital Ship. Will not work if no Capital Ships have been lost. Cannot be used by Progenitor on itself. (100/75AM, 120/90sec)
Advent (Rapture Battlecruiser)
Vertigo: Reduce the weapon accuracy and weapon cooldowns of hostile frigate or corvette (4500/5110/5720/6325 km range) and all those within 2000/2485/2970/3450 km by 10%/18%/26%/34%, for 25 sec. (75AM, 20sec)
Vengeance: Targetted friendly non-strikecraft within 6000 km retaliates 65%/120%/175%/230% of any damage it receives to the attacker for 20/39/37/46 sec. (70AM, 30/37/45/52sec)
Concentration Aura: (Passive) The strikecraft belonging to friendlies within 8000 km do 10%/18%/26%/34.5% extra damage.
Domination: Take control of target hostile frigate within 6000/7500 km. (150/112AM, 60sec)
Advent (Revelation Battlecruiser)
Reverie: Disable hostile capital ship or frigate within 8000 km for 20/29/37/46 sec or until it takes 200/287/373/460 dmg. (75/75/65/65AM, 15sec)
Guidance: Friendly non-corvettes/strikecraft within 8000 km have their ability cooldowns reduced 25/30/35/40% for 20/25/30/35 sec. (90/100/110/120AM, 50sec)
Clairvoyance: View target system for 90/118/145/175 sec, infinite range. (70/60/50/40 AM, 15sec)
Provoke Hysteria: Reduce the health of target hostile planet within 5000 km by 1%/1.25% per sec, and population by 0.75%/0.86% per sec for 40 sec. (150AM, 180/135sec)
Advent (Discord Battleship)
Fracture: Reduce the armor of the target non-strikecraft ship and all those within 3500/4000/4500/5000 km by 2/2.5/3.5/5 for 20 sec. (45AM, 30sec)
Psionic Scream: Deal 100/200/300/400 (125/250/375/500 with fracture) damage to targeted capitalship or frigate within 4500/5000/5500/6000 km and all those within 3500 km, and also disable their abilities for 3/4/5/6 seconds. (90/85/80/75AM, 25sec)
Lethargy: Increase weapon cooldown by 10/15/20/25% and ability cooldown by 25/33/41/50% of targetted titan/frigate/capship within 4000 km for 15 sec. (24AM, 25sec)
Revenge from Beyond: Cast on friendly frigate within 8500km. Does 450/650 damage to all hostile non-corvette/strikecraft ships within 8000km when the target dies. (150AM, 160sec)
Vasari (Kortul Devastator)
Power Surge: Decrease own weapon cooldown by 25%/45%/66%/86% and restore shields per second 25/34/43/52 for 20/25/30/35 sec. (60AM, 30/35/40/45sec)
Jam Weapons: Disable weapons of hostile strikecraft within 4500/5500/6500/7500 km for 20 sec. (70AM, 40/35/30/25sec)
Disruptive Strikes: (Passive) Every shot has 30% chance increase on hit to increase hostile's cooldowns by 17%/30%/44%/57.5% for 15 sec and remove 12/22/32/41 antimatter.
Volatile Nanites: Target hostile non-strikecraft within 6000/7500 km and other hostiles within within 2000 km of it take 30/37.5% extra dmg for 60 sec. and deal 150/187 dmg on death to nearby hostiles within 1000 km. (150AM, 180sec)
Vasari (Skirantra Carrier)
Repair Cloud: Repair 20/25/30/35 hull per sec for 10/12/14/16 sec (200/300/420/560 total repaired) on friendlies within 3000/3530/4070/4600 range. (100/90/80/70AM, 12sec)
Scramble Bombers: Create 1/2/3/4 squadrons of bombers for 75 sec. (50AM, 30sec)
Microphasing Aura: (Passive) Friendly strikecraft within 8000 km have a 20%/30%/30%/35% chance of teleporting 750km close to their target, making them invulnerable for 1 sec, every 4/4/3/3 sec.
Replicate Forces: Instantly produce 3/4 copies of target frigate you own, for 150/175 sec. (125/100AM, 180/160sec)
Vasari (Jarrasul Evacuator)
Colonize: Colonize target planet, and create 1/2/3/4 additional construction frigates for 240/436/632/828 sec. (90AM, 120/97/74/51sec)
Gravity Warhead: Target non-strikecraft ship within 6000 km, and all those within 3000/3533/4066/4600 km of it, have its phase jump disabled, max speed reduced by 30%/43%/56%/69%, and acceleration reduced by 60%/86%/112%/138% for 12/15/18/21 sec. (100AM, 25sec)
Nano-Disassembler: Deal 25 hull dmg per sec to target non-strikecraft within 6000 km and reduce its armor by 1.5/2.7/3.6/5.2, for 25/32/43/52 sec. (75AM, 12sec)
Drain Planet: Deal 45/51.75 dmg per sec to, kill 2/2.3% population of, and steal 15/17.25 credits per sec from target planet within 6600 km, for 30 sec. (150AM, 180sec)
Vasari (Antorak Marauder)
Phase Out Hull: Target friendly or enemy non-titan/strikecraft within 7000 km is disabled and invulnerable for 6/8/10/12 sec, and takes 200 shield damage (enemy) or receives 200 shield points (friendly). (60/55/45/35AM, 5/4/3/2sec)
Distort Gravity: Antorak and nearby friendly capitalships/frigates/titans within 5000 km increases max speed by 33%/55%/77%/100%, increases linear acceleration by 50%/66%/83%/100%, increases angular thrust by 25%/45%/63%/86%, become immune to phase inhibitors, and can phase jump 8%/15%/21%/28% further from the system edge, for 30 sec. (65AM, 45sec)
Subversion: Increase ship & structure build time of hostile planet by 50%/91%/132%/173% for 300%/430%/560%/690%. (100AM, 75sec)
Stabilize Phase Space: Creates a Phase Stabilizer in current system for 75/94 sec. (100/75AM, 120/90sec)
Vasari (Vulkoras Desolator)
Phase Missile Swarm: Deal 200/363/527/690 dmg to 4/7/11/14 hostile non-strikecraft in target area within 6500km. (90AM, 15sec)
Deploy Siege Platform: Deploy siege turret for 180 sec near target hostile planet within 2600 km. Has 735 hull, 2 armor, and does 20/26/31/37 bombing damage and 1/2/2/3 population damage. (35AM, 20ec)
Assault Specialization: (Passive) This Vulkoras does 90/164/237/311 extra damage per hit against structures (12.85/23.42/33.85/44.4 DPS boost), and bombs planets 25%/50%/75%/100% faster.
Disintegration: (Channeled) Heals 1500 shields and hull, restores 120/152 antimatter to self, drains 160/200 antimatter and deals 1200/1504 hull and shield damage over 8 sec to target hostile non-strikecraft within 6000 km. (150AM, 90sec)
Vasari (Rankulas Battleship)
Create Combat Swarm: Creates combat swarm for 180sec. (40AM, 30sec)
Create Support Swarm Creates support swarm for 180sec. (40AM, 60sec)
Create Assault Swarm Creates assault swarm for 180sec. (40AM, 90sec)
Reassemble Combines active swarms into a greater swarm with bonus hull/shield/weapons based on the number of swarms combined. (150AM, 90sec)