CastDetailsView: Use controller content manager within the details view

Create an instance of MediaRouteControllerContentManager within
CastDetailsContent to manages showing the content of the cast controller
when 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: Ib4e956857a423cb8e8eef24b2ddda2f04c3d16c3