leaudio: Remove reduntant context type copy

With latest aligment of context type between directions, it is not
necessary to set local_metadata_context_types_.sink when
local_metadata_context_types_.source has changed.

This actually can break future context type when we set context type
with high priority e.g. CONVERSATIONAL

Bug: 367894783
Flag: Exempt, regression tested with unit test
Test: atest bluetooth_le_audio_client_test
Change-Id: I957b331f0bfd7b8d60b971fcf0e7903004ae480f