[SB][Screen Chips] Convert CastController logs to LogBuffer.

The new screen chips rely on some data from CastController, and it would
be great to always have that log information available in a LogBuffer.

Bug: 351785188
Bug: 332662551
Flag: NONE logging change

Test: Do some cast interactions then dump `CastControllerLog` -> verify
logging
Test: atest CastControllerImplTest

Change-Id: Iab36b4df3399ab6260213d5733fdb517f0b0e4f0