> As for errors in siblings aborting the TaskGroup, could you apply a wrapper to the scheduled coroutines to swallow and log any errors yourself?

Yes, this could be a simplest way to implement PersistentTaskGroup if TaskGroup supports "persistent" option to keep it running.

And just a question: I'm just curious about what happens if belonging tasks see the cancellation raised from their inner tasks.  Sibling tasks should not be cancelled, and the outer task group should not be cancelled, unless the task group itself has requested cancellation.  Could the new cancellation counter help this?