Improve Plugin Logging and refactor out a core logging lib

Normally there'd be related changes to SysUI Studio, but the gradle
build files don't differentiate between the Plugin Lib & Plugin Core
Lib, so they also don't need to differentiate between the Log Lib, and
the new Log Core Lib.

Bug: 389987229
Flag: NONE Build Reorganization
Test: Checked existing functions
Test: test_gradle_build.sh
Change-Id: I6ad4502d5d3342214ef9246f571c00583a59f503