le_audio/client: Fix RemoveWhileStreaming test

The order of operations was getting randomly mixed up
due to race condition between tester thread and main loop.

To fix this we put the tested command on the main loop as well.

Bug: 266872728
Test: atest bluetooth_le_audio_client_test
Tag: #feature

Change-Id: I4f9af01a411b3a0914145e7ade54d8fef039cc48