[ROSP] Use Hydrator and AssistedInject for MediaControlChipViewModel

This change refactors `MediaControlChipViewModel` to utilize snapshot
state instead of exposing a flow.

Bug: b/394887130
Flag: com.android.systemui.status_bar_popup_chips

Test: atest MediaControlChipViewModelTest
Test: Make sure media chip shows up in the status bar.

Change-Id: I5c93c244116360fee6939d0464eb609654bd244a