[LE Broadcast] Add the active LE device into broadcast when broadcasting

- Add the source into active sink device when user start the
  broadcasting.
- Add a flag to avoid re-register callback of broadcast.
- Register/Unregister the assistant's callback.

Bug: 246761387
Test: local test
Test: atest MediaOutputBroadcastDialogTest
Change-Id: I7326a3d299943de2ede144f12d2b663c915dd304