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.