Clean up unused functions in MediaRouteControllerDialog

A couple functions and variables in MediaRouteControllerDialog is
currently unused. This is legacy code and should be removed.

Also did some improvement in casting and variable usage within the
class.

Test: manual, open Quick Settings, click on Cast tile and check dialog
Bug: 395947047
Flag: NONE clean up legacy code
Change-Id: I1d8f418f9f730da6b6e3296d421b8eb1d2e912ee