My builds have finally finished processing, and are now visible on TestFlight. I’m curious, is this a common occurrence that we should be aware of? What was the reason for the unusually slow processing time? Would be nice if we had some indicator of the progress of a build’s processing phase, so we can be sure as developers that we haven’t done anything wrong and just need to wait.

Same here, our builds are not successfully processing through App Store Connect, since noon ET today at the earliest. They are successfully uploading to App Store Connect, but they do not appear at all on the TestFlight page. We have Xcode Cloud builds running that should be deploying builds to internal & external testing on TestFlight, and they successfully archive and save the artifacts (green check in the Xcode Cloud log), but are not showing up in the list of downloadable artifacts in the Xcode Cloud build logs. Those builds made on Xcode Cloud are also not showing up in TestFlight, and the Xcode Cloud workflows get stuck and continue running ad infinity, running up our hour usage. We have tried from 2 separate developer machines to manually archive and upload, and those builds successfully uploaded, but have not yet appeared on App Store Connect on the TestFlight page. Really hope this is resolved soon, it's a major inconvenience to our release process.