I just plugged the mouse into another USB slot and that seems to have solved it.
I feel a bit stupid for not having tried this earlier, but I also don't understand why that is a thing.
If the problem reoccurs, I'll report it here. Otherwise, this case seems closed.

Hello engineers,
after a couple of years, I decided to come back for space age.
Unfortunately, I am now plagued by very annoying mouse freezing / stuttering.
It happens in main menu (with background simulation) as well as in the first tutorial mission (and probably all other game modes).
When I ...