I am also having the same issue. I've reported it via the feedback forums, but essentially: Xcode cannot generate provisioning profiles that include the com.apple.developer.activitykit entitlement, even when the app is properly configured with ActivityKit capabilities and entitlements. I can't even see ActivityKit within the developer portal. I'm unable to distribute apps with Live Activities through App Store Connect or TestFlight. This affects both Xcode automatic signing.

I'm starting to think this is a manual approval process by Apple as I've tried everything to get this to work at this point.

I got a response and it was to read the documentation... no matter even if I start a new project, ActivityKit is not there.

Apple have reached out, I'll be in touch with any updates if I manage to get it working.

Not yet @Pavel_Suchkou - I've sent a bunch of logs to Apple, hoping to hear back this week.