This is only true for us if the live activity was started from the app.
When the Live Activity was started from apns, then PushTokenUpdates will only emit new tokens if user hits on "Allow" from Lock Screen. Toggling OS permission off and then back on won't cause how Apple evaluates — at until now.
I think is a bug. Since the docs on PushTokenUpdates say:
By default, your app can start, update, and end a Live Activity if you use ActivityKit to offer
/// Live Activities
Topic:
Accessibility & Inclusion
SubTopic:
General
Tags: