LeAudio: Fix updating current scenario context

Even when a new scenario leads to the same configuration
that is currently set and no actual reconfiguration is
needed, we should update the scenario context, so that
it would not be confusing on what the latest scenario is.

Bug: 285647765
Test: atest bluetooth_le_audio_client_test
Change-Id: I8d1c8a893afe395dd03514c23d49d25d503bba28