Just a follow up. I walked my boss through the process of submitting to TestFlight Beta with their "Account Holder" account and everything worked fine without issue for them. I've been using TestFlight since before it was cool, since before Apple's 2014 acquisition of the service. So the fact that I'm totally blocked for what should be my 40th or 50th Beta release seems very weird. Therefore, the issue I'm experiencing seems to be related to either: Just my account on our team, or the "App Manager" et al permissions level in general perhaps (maybe I'm missing an announcement about a recent(?) change), or the TestFlight backend is experiencing problems? Regarding that last point about the stability of the backend, Apple's Status Page showed green checkmarks all the way down at the time. Apple is usually pretty good. AWS, on the other hand, has set the bar for how untrustworthy a status page can be. But I definitely have more faith in Apple than AWS so I went ahead and walked my boss through the TestFlight Beta release process. While we did this walkthrough, I periodically reloaded the TestFlight portal on my side and noted that I was still seeing a seemingly broken UI.

The issue appears to be resolved. The following may just be a coincidence, but I'll describe what I did before it started working. I have two developer accounts on my employer's team account. One account for my company email and one for my personal email Apple ID. Again, might just be a coincidence, but I tried signing out of my company email account and signing into App Store Connect->TestFlight with my personal Apple ID. At which point, I had access to update the test information and add external testers! I then signed out of my personal account and signed back into App Store Connect with my default company email account. And I had access to update the test info and add external tester groups as well. Before I tried all this signing in-out stuff, I had already confirmed this morning that I was still seeing the issue. Either Apple fixed this issue later today or [queue magical thinking now:] I was hitting some sort of caching/cookies conflict or something? So if you're still seeing this issue and you have two+ accounts on the same team, you may want to try logging out of one and logging back in with the other, assuming they have comparable user levels.