Encapsulate call to beginBroadcast in synchronized

beginBroadcast cannot be called concurrently.
When shuting down the profile, multiple profiles can try to broadcast
their state to proxies which can create a crash.
There was a attempt to prevent that with a boolean, I am replacing it
with a synchronized block

Bug: 272430969
Test: atest ServiceBluetoothTests
Change-Id: Ie840cbf303c1f44d1aa254da798c8ff30d7d0fc9