I am seeing the same thing. The notifications are in the order that the device received them regardless of the relevance score and content of the message. The relevance score is correct when I debug/log it in the notification service extension so it really seems like an iOS bug. I tested this with the Xcode 13.0 rc and iOS 15 release build.

I have been testing the Live Activity API using the latest betas and the activity is saying it is started correctly, but is only displayed if it is the only widget in the extension. Can you have multiple widgets and live activities at the same time? I am also never getting a push token when starting the activity despite having push setup and being on an eligible machine according to the note in the doc. Has anyone gotten a live activity to properly display and/or a push token?

I have gotten it to show on a real device and have gotten push tokens now. It does seem like you are not able to start a live activity from the background which was not documented. If anyone has a way to do this that would be great to know!