Bluetooth: MPL: Replace busy bool with atomic

Replace the busy boolean flag with an atomic value.
This prevents any race conditions with the MPL implementation.
Modifies where the new atomic value is set and cleared
so that initialization gets to finish before allowing
any reads.

Due to how the MPL is structured, and how a select cannot
be rejected from OTS, this does not give a perfect solution.
Ideally we need a separate object per OTS object, rather than
a shared one, and/or the OTS implemenation would allow
us to reject a select if the object is not currently
available or ready.

This commit does not fix the above issues, as that is a
larger undertaking.

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