Nothing bad hapens when removing TestFlight, it just handles the install/updating of those apps. They even still open fine if you remove it, and when reinstaled it imediatly knows whats installed and whats not just like before.

Signing out of the AppStore, removing the device using another device's TestFlight install (you cant remove your own device from TestFlight), rebooting and re logging in to the AppStore and reinstalling TestFlight seemed to fix it, but only for a very short time. After a day it started happening again and this time redoing that procedure on 2 different devices didn't make a difference. Seems like a backend and/or TestFlight app issue, hopefully its resolved soon.

Do you by change know if auto TestFlight app updates while plugged in worked during that time, and if not, did they start working after?