Properly mark asyncStart situations

While not likely, there is a chance that other asyncStart
situations happen during a chain (since these are leaving
the global lock after-all). So, just in case, properly
push/pop asyncStart tracking even tho there's no chain
logic yet.

Bug: 325114242
Test: existing tests
Flag: com.android.window.flags.transit_tracker_plumbing
Change-Id: I7cb7275f0799141c6b9e0384116a1794a38d1ae5