Looks like it works as expected sometimes (maybe most of the time?) but sometimes doesn't. In the video below, only the transport group would revert selection back to my assault group when clicked

Merely to supplement and confirm the behavior mentioned:

In a new session, I can switch between the default groups exactly once. Further switches aren't possible. After that, I can't create a new group either. I’m essentially stuck in that one group—no matter what I try to do to get out of it.

As long as I haven't switched from the initial group, I can—as usual—create a new group and join it. However, if I die and respawn, the newly created group is automatically deleted; I end up in the "reserves" group and get stuck there, too—meaning I can't leave or switch out of that group either.

However - i got the hint from HERO in discord, that navigating in group menu with keyboard works as expected - and it does.