Revert^2 "Avoid locks in various singleton HandlerThread types"

This reverts commit 4f5e3078.

Reason for revert: Reland w/ fixes for sHandler init assumptions from Robolectric tests

Test: atest WearServicesRoboTests
Test: atest WearSdkRoboTests
Test: atest ClockworksFrameworkRoboTests
Bug: 411249866
Bug: 414673812
Change-Id: Ief1dec13d08a73d32f7d804a6c21c64cf196dd07