Reland "CastDetailsView: Use controller content manager within the

details view"

The original CL was reverted due to b/403313655. This is a clean reland
with no change needed.

Bug: 378514236
Flag: com.android.systemui.qs_tile_detailed_view
Test: CastTileTest
Test: Click on cast tile in the QS -> the cast controller show up
correctly in the details view

Change-Id: Id1033f12a3d363a18c321fb62ced2bfd61dac5f0