le_audio_software_aidl: Fix race condition on start request confirm

Uses atomic compare and exchange to avoid cases where the confirmed
stream request is not registered and overwritten. This happens when
the other thread confirms the request after we already checked the
state, but before it is set here.

Bug: 258127534
Test: Manual testing
Change-Id: I3528e97d6944949bf5031975b9f8e436db68aa3c