CastDetailsView: Show up cast chooser UI within the details view

Add the support to show up the chooser UI within the cast details view.
This includes showing R.layout.media_route_chooser_dialog within the
details view UI, as well as initializing a
MediaRouteChooserContentManager instance to control the backend
behavior.

Bug: 378514236
Flag: com.android.systemui.qs_tile_detailed_view
Test: CastDetailsViewModelTest, CastDetailsViewContentTest
Change-Id: I8011ae6c3ef3729aa814a936d35072a34a519c6a