[tool] Extract most conformance checks to separate validator classes (#11610)

Extracts the logic for many of the lightweight, repo-practice commands into separate validator classes, leaving just a minimal amount of logic in the command, in preparation for combining all of these into a single command. Doing so will make running conformance checks locally much easier since there will be fewer commands to run, and will make documenting both the tool itself, and the commands we want run against PRs (e.g., for agent instructions), easier as well.

This is a mostly no-op code move, so that tests can change as little as possible in this PR. Then the next PR will then combine the commands, which will require a lot of test changes, but almost all of the non-test code will be able to stay unchanged because it's in the separate validator classes, which the combined command can call into as they are.

All the new files were created by moving code from the corresponding command file, with very minimal changes (e.g., sometimes context that was a non-private getter from the base command class is a private field in the validator class, so underscores were added.) This is reflected in the fact that there are almost no test changes.