[Screen share] Update our status to "projecting" earlier in process.

In the old screen share icon, we started showing the icon as soon as
MediaProjectionManager.Callback#onStart is called. With the new screen
share chips, we only started showing the icon when
MediaProjectionManager.Callback#onRecordingSessionSet is called. If a
user is only sharing *audio* to an app, but not their screen,
the #onRecordingSessionSet method is never triggered but we should still
show the screen share chip.

Bug: 373308507
Bug: 332662551
Flag: com.android.systemui.status_bar_show_audio_only_projection_chip

Regression tests:
Test: Screen record single app -> verify chip does 3-2-1 countdown then
starts timer, has screen record icon
Test: Screen record full screen -> verify chip does 3-2-1 countdown then
starts timer, has screen record icon
Test: Share screen to app that does a 3-2-1 countdown -> verify chip
starts showing with just share-to-app icon, then shows timer after 3-2-1
countdown is done
Test: Share screen to app that immediately starts recording -> verify
chip timer immediately starts
Test: Cast screen to another device -> verify chip shows cast icon +
timer
Test: Cast audio to another device -> verify chip just shows cast icon

Test: atest MediaProjectionManagerRepositoryTest

New test:
Test: Share *audio* to another app -> verify chip shows, and has
share-to-app icon

Change-Id: Ifa84ec811ef3456792a3cd6b7766d6c738536af2