When using the ManagedSettings API to block apps everything is blocked as expected (the app itself, Notifications, Live Activities on the Lock Screen etc) except for Compact Live Activities of those apps (that are shown in the Dynamic Island). I feel the expected behavior would be to block also the Compact Live Activities.
Our use case: In Spoilerblock we want to prevent users from being exposed to spoilers before they've had time to watch for example a sports game.
Current workaround: Right now the best we can do is to ask the user to disable Live Activities for apps that could expose results, to not risk being exposed to a spoiler.