This issue starting happening to me today as well. Created a new internal beta group, added myself to it, and was able to assign that group to the new build. However, build does not show up in TestFlight and it has been about 5-6 hrs.

I was able to resolve the issue in my case, by adding "App Uses Non-Exempt Encryption" to the Xcode project Info.plist I had been just clicking the 'manage compliance' link that would be shown by every build I uploaded, and that had always worked fine. As soon as I added the "App Uses Non-Exempt Encryption" key & value ('NO' in my case) to info.plist, the next build I uploaded to App Connect was delivered within a couple minutes to TestFlight.

Make sure you have "ITSAppUsesNonExemptEncryption" key in your plist.info file in Xcode build, with a value that matches your project (either NO or YES). Yesterday I found that not having that key/value already in the plist.info file blocked my builds from going to TestFlight, or assigning Internal test group. It didn't seem to matter that I clicked the 'manage compliance' and answered the build encryption question post-processing. As soon as I added the key/value to my plist.info, I could assign internal testers to the build, and it deployed right away to TestFlight.

https://developer.apple.com/forums/thread/778161

Same frustration yesterday, see solution that has worked for me and others: https://developer.apple.com/forums/thread/778161

There are 3 threads below this one on the same issue, see possible solution in those threads.

https://developer.apple.com/forums/thread/778161