Prepare filter for moving to shared

[srawlins]

Work towards https://github.com/flutter/devtools/issues/7793

In this CL, we are just preparing this code to be moved into shared code, but it is not shared here.

I tried to make as much private as possible. That is, when there are methods or fields that are currently only used privately, I make it private, with the idea it is not an API appropriate/necessary for public consumption. In a few cases, a method or field is used privately and in tests. In those cases, I made APIs @visibleForTesting.

I also adjusted comments a bit, as these will be published documentation.