Migrate from `mypy` to `ty` for type linting

I noticed in working through #328 that `mypy` sometimes seems to over-react about type linting checks and provides challenging guidance with concerns to fixes. I feel we should move to more modern type linting tools such as [`ty`](https://github.com/astral-sh/ty) to help avoid these challenges and keep development velocity high.

The issue names no files, tests, or CI entry points. Start by locating the repository's current mypy configuration and linting invocation, then determine how ty would replace them. Done means type linting runs with ty, mypy is removed from the relevant setup, and the existing checks pass.

Written by the indexing model from the issue text.