Every time there's a battle, a small popup window shows up in the main map screen. This screen shows the forces fighting.

At the bottom, there are two options. Pick the "Quick Battle" option. That resolves the fight without going to the cinematic viewer.

I mean I wish it were 5 seconds instead of 10 (or half what it really is), but you can do other things, you don't have to watch it. Just can't order ships I think, which I agree, is annoying.

I could do something else, but I can't start another attack .... for example....
In first/second/third mission from campaign I moved to the point that I haven't enough ships to attack enemy planets, but I have enough ships to destroy enemy spacedock (which enemy build every 2 turns), it was two docks near two enemy planets. It was very annoying to destroy stardock every 2 turn and wait for research / better ships from my docks .....