I tried to deactivate first(failed with error code 5 multiple times), uninstalled successfully, rebooted right after that, 
installed Start11v2 2.52 beta, activated, found the bug still exists by just one trial, rebooted, and also found that this bug still exists.

However, 2.52s behavior is somewhat different if I remember right.
In this version, both tiles and list got locked, but it seems like it's under racing condition to other processes because at bugged state mousehover animation "sometimes" do play occasionally on both tiles and lists. I was able to escape from this bug by trying to type anything and removing texts to call and close Start11 search multiple times. One trial may not unlock it, but several times of trial, it worked. Sometimes, lists and tiles returns to be usable state without I do anything. Sometimes, it doesn't.
In this version, I can't 'execute any program on the list' to unblock it, because this time list also got locked. 

My CPU load wasn't high. While I tested those, my computer was almost idle, had a plenty of CPU scheduling to process Start11 and one Chromium browser servicing this forum. Looking from its mousehover behavior, it looks like both tiles and lists are on a racing condition to Start11 search feature. Waiting long enough until search provides results doesn't help, it sometimes locks it. Typing something and immediately backspace to null, also sometimes locks it, and sometimes it unlocks them to usable state. HDD load does not seem to matter also. I tried to backspace to return to Start menu after HDD head noise stops. It still trigger, sometimes.

With 30 minutes of use, I didn't found Start11 configuration window locks or do racing with Start menu lists and tiles.

Also, I found that left side list's mousehover effect sometimes does not get cancelled on time when mouse cursor is traveling outside(mainly to tiles section in Start11 Windows 10 style). Those mousehover'ed lists eventually updates their stales right, but not on time they should be.
Yes, it's 'sometimes' again. Not every mousehover exit leftover remains out of time table.
If mouse travels to empty spaces or tile group name bar at tiles section, this doesn't seem to be triggered. If mouse travels to tile buttons, it triggers.

Sorry for bad English, I know it's recursive but I don't have enough time to review texts today.

1. Touch mode UI scaling: [Force not touch mode device] worked for me from getting away from scaling bug. I didn't felt comfortable using it anyway. 
For that case: 150% UI scaling monitor + 100% UI scaling tablet may triggered wrong behavior of Start11. I don't see that recently after I posted this thread.

2. Lockup:

Still happens occasionally. I still can't find exact trigger. It's not 100%, sometimes 25%, mostly 10% for me. 
If I call context menu at locked up tiles, the only menu I can see is Start11 configuration.

(New discovery) When it triggered, top 3 list items at the left side list, and tiles placed at same height worked but at the height of fourth list mouse event does not work at tiles.

Image: Rough estimation of height that is working or not. Above red line seem to be working when tiles and lists are blocked access from mouse, when I backspace sdfasdf at top search textbox.

Just in case if it helps, My options at Start11 Search feature: 
(Rough translation, my WIndows is running in Korean language and Start11 is also running in combination of Korean and English)
1. I use Start11 search at Start11 start menu.

2. Enabled: Option 1 Show search result filter icon
3. Disabled: Option 2 search name and contents (slow)
4. Disabled: Option 3 Search for shortcuts on the desktop and in Fences
5. Enabled: Option 4 Include Microsoft Edge opened tabs in search result
6. Enabled: Option 5 Show Everything search results instead of Start11 file search
* I have Everything installed and running.

7. Disabled: Use old Start10 style search

Something is covering lists and not releasing itself on time occasionally...

Also, I'm still on 23H2. Thankfully MS don't want me to go through buggy hell 24H2 yet.

Hmm, in my case, to make wheels work when it's stuck, I have to move a mouse cursor outside of stucked area.

Also, reopening Start11 start menu does not resolve.

Image: The 2/3 zone line.
I'll say Left Zone includes vertical button array which one contains Power, UWP Windows Options, Explorer, etc., and lists divided by that red line. I think it's about 2/3 but I'm not sure about its exact length.

One more discovery after watching your video:
When I move my mouse to the [Left Zone], Left app lists back in action for mouseover and clicks, but mouse wheel only works when mouse cursor is located at [Left Zone] but inside the app lists. Once I move the mouse cursor to tiles area, entire app lists except top 3 rows return to stuck state before I move the cursor to [Left Zone] at the image above. Mouse wheel is stuck also.

Hi Aricia,

It seems the issue is when backspacing out of the search, the menu loses focus, which prevents the mouse from interacting with it until the focus is regained. 

I've reproduced this and logged for review.

Internal Ref: ODNT-9883

Best regards,

Adam McGuinness
Stardock Customer Support Specialist