[Screen share] Make start button text be option-specific.

With the new dialog UX, the start button text is different depending on
whether "single app" or "entire screen" is selected. This CL makes that
text be set when an option is created, and also updates the cast dialog
to use different text in the two cases. (Record and share updates will
be in a future CL.)

Bug: 352327853
Flag: NONE string changes
Test: Cast screen to other device -> verify start button text is "Next"
when selecting single app option, but "Cast screen" when selecting
entire screen option
Test: Screen record -> verify start button text stays the same
Test: Share to app -> verify start button text stays the same
Test: atest SystemCastPermissionDialogDelegateTest

Change-Id: Ie4bbe23826f0862beda73d69536f9a74e84e1983