I couldn't find a logging library that worked for my library, so I made one

It's Strings. They go somewhere. The interface writes itself: Consumer<String>.

At my absolute fanciest, I use a Queue, some terminal colouring, separate stderr from stdout, and write some short-hand functions (warn, err, info, etc.).

These are the bugs I don't have: https://github.com/apache/logging-log4j2/issues