Bluetooth: BAP: BA: Replace bools with atomic

Replace the boolean values for the BAP Broadcast Assistant
with an atomic value. This prevents a rare, but possible,
race condition.

The busy flag has been replaced with 3 atomic values which
provide better granularity in error handling, and allows for
some concurrent write and read requests.

To describe the new behavior, the return values in the documentation
has been updated, and the error handling in the API
functions has improved.

Signed-off-by: Emil Gydesen <emil.gydesen@nordicsemi.no>