Same story - I do see the button for one app and I don't see it for another app. Both apps are built with Xcode 13, as far as I know. Wondering if it might be related to difference in the build settings or to the fact that the app that has no download button employs Fastlane for upload to TestFlight.

Thanks for mentioning this trick with figuring out CODE_SIGN_IDENTITY, @m-miscampbell! Unfortunately, I could not get it working because it looks like it conflicts with automatic code-signing.