Bluetooth: Mesh: Fix async behavior of Private Beacon Client API

The Private Beacon Client API requires a response argument to allow to
call the API in the asynchronous manner
(https://github.com/zephyrproject-rtos/zephyr/pull/56426).

Because the removal of the EXPERIMENTAL tag for this API was not
released yet, it should be OK to change this API.
The EXPERIMENTAL tag has been removed here:
https://github.com/zephyrproject-rtos/zephyr/pull/64866



Coverity-CID: 330039
Coverity-CID: 330029
Coverity-CID: 329977

Fixes #65336
Fixes #65338
Fixes #65354

Signed-off-by: Pavel Vasilyev <pavel.vasilyev@nordicsemi.no>