[Dual Shade] Refactor ShadeHeader's view-model and clock interactor.

This CL modernizes and simplifies some of the state flows in the shade
header code, separates concerns better between the interactor and view-
model, and adds missing unit tests for the calculation of the current
time.

Bug: 397197000
Bug: 397195068
Test: Added unit tests.
Test: Existing unit tests still pass.
Flag: com.android.systemui.scene_container
Change-Id: I85b99ca7c1cb60272f6a9a7c7d312af5dd541e27