[ROSP] Use Hydrator and AssistedInject for StatusBarPopupChipsViewModel

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

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

Test: Make sure popup chips show up in the status bar.

Change-Id: I89dc8971fcaa39992f7065526aa14a312f2d22c7