[SB] Rework chip visibility & notification icon visibility with HUNs.

I noticed a few problems:
 - With StatusBarNoHunBehavior flag off, if you have a chip and then get
   a HUN then we weren't showing the HUN's notification icon because
   `isAnyChipVisible` was `true`.
 - With StatusBarNoHunBehavior flag on, then tapping the chip to show
   the HUN would hide the chip because there was a pinned HUN.

This reworks the flows to address both of these problems.

Bug: 364653005
Flag: com.android.systemui.status_bar_no_hun_behavior
Flag: com.android.systemui.status_bar_root_modernization

Test: NoHunBehavior off: Verify status bar updates to show HUN icon &
text if you have a chip AND if you don't have a chip
Test: NoHunBeahvior on: Verify status bar always shows clock & chip,
even if there's a chip HUN showing or a non-chip HUN showing

Test: atest HomeStatusBarViewModelTest
Change-Id: Ie58ebbc9ad021f9e33b1280c4cbbc4d146b31e23