I have run into this problem today. I distribute a macOS app to internal testflight group from Xcode. Upload to App Store Connect succeeds. I receive the email that a new TestFlight build is available to test in TestFlight. The new build shows in TestFlight app. When I try to install the build I get the following error dialog.
Could not install App. TestFlight is currently unavailable. Try again.
I have submitted feedback FB24059381 with additional information.
Hello there! Thanks for reporting this. This should now be resolved.
If you're still unable to unable to install and test your apps, please file a Feedback Assistant with screen recordings and sysdiagnose logs attached, and paste the number here.
We'll be happy to take a look.