[Misc] Move screen recording flow to general repository class.

For the status bar screen sharing chips feature (b/332662551), the
status bar needs to know the state of screen recording just like the
quick settings tile does. This CL moves the screen recording state flow
into a generic repository in the generic `screenrecord` package, and
updates the tile interactor to listen to that repository.

A future CL will re-use this repository for the new status bar chip.

Bug: 332662551
Test: atest ScreenRecordTileDataInteractorTest
Test: enable qs_new_tiles flag and verify screen record tile still works
(can start and stop recordings with it)
Flag: com.android.systemui.qs_new_tiles

Change-Id: I67e214ec1103a524265e9a0f10dc519d4f8d9e18