Our company is facing the same issue. After App is built and uploaded to the testFlight apps don't get assigned groups, can't download them in the testFlight, can't do anything with them.
Blocking entire testing workflow and release workflow.
I am personally seeing several other errors today, with user access management, viewing distribution tab in appstoreconnect gives error sometimes(but resolves on a refresh). But testFlight app processing issue is the most important to fix.
Topic:
App Store Distribution & Marketing
SubTopic:
TestFlight