Replace verifyproblem classes with models + checks

[gkreitz]

This completes the large refactor of splitting verifyproblem into manageable chunks (models + checks) we can more easily work with going forward. Here, we remove all the ProblemPart classes (which were all seams at this point), and replace the whole thing with a thin new class, ProblemVerifier.

There will be follow-up PR:s to fix and clean up things in various checks which I didn't do while extracting functions. My hope is that this is a better foundational design to work from (and cleaner to use as an API).

Added in adjusting the type of the temporary work directory we set up for checking to be Path. As it's now Path in verifyproblem, it ended up very silly to cast it to str to pass it to checks to there cast it back to Path.

Fixes #398