It’s strange that you can’t reproduce this problem on Big Sur 11.5.2.
I did what you said: disabled TeamSpeak in the Accessibility tab, quit TS and restarted it.
It didn’t ask me to allow anything (I think it only did during installation). So it is not in the Accessibility tab.
So it is impossible to create a shortcut.
So I put TeamSpeak back into the Accessibility tab (with its box checked automatically), quit and restarted TeamSpeak: no change.
Finally, I restarted my Mac, skipping the PRAM - to no avail.
I have a brand new Mac with a clean install (nothing from a backup of any kind) and I can guarantee that I did nothing special.
I even uninstalled TS with Clean My Mac to make sure there was no code left and reinstalled it (this time it asked me for accessibility) but still without the ability to create shortcuts
You must have done something you don’t remember (or are you on a hackintosh?).