From your description in your other comment, you probably don't have the same problem as we have: you get the round circle and nothing happens. We jump back immediately to the "Update" icon when taping on it.
I’ve occasionally seen the round circle, but it never progresses and eventually goes back to a spinning icon and then the update button. This can happen if I do an update all.
Normally though, I just get the spinning wheel and the update button again.
Dave14305 said his is working now though, so it might be a different issue.
Also my Apple ID isn’t a developer account. I’ve just tested TestFlight apps on it.
I asked some other beta testers of the apps I’m testing and they say they are logged into the Sandbox account, but not having any App Store issues.