Remove the dependency on SystemServerInitThreadPool from IMMS

With this CL we start calling

  AdditionalSubtypeMapRepository.startWriterThread()

without SystemServerInitThreadPool, as it is supposed to be fast and
simple enough. It is the last dependency on SystemServerInitThreadPool
in the InputMethodManagerService.

This is a minor cleanup on how the background writer thread is
initialized. All the observable semantics should remain unchanged.

Bug: 343601565
Bug: 350790602
Test: presubmit
Test: atest FrameworksInputMethodSystemServerTests
Flag: EXEMPT refactor
Change-Id: I16e29c1d008850bd1ea20fb1e36fb483b0ca38fe