Restructure codebase to add widget tests

Intention is to refactor project to add widget tests, considering benefits, and incremental changes towards this. I'm not sure how to make this a clear and complete issue, so I'll keep notes at wiki linked here:

- https://github.com/bradyt/taskw-dart/wiki/Refactor-to-add-widget-tests

Start with the linked wiki page, “Refactor to add widget tests,” because the issue body says the implementation notes are maintained there. Use those notes to determine the incremental refactoring scope and what widget-test coverage is expected; the issue does not name files, tests, or a completion criterion.

Written by the indexing model from the issue text.