Evaluate Python type checker alternatives to mypy

# Context

We currently use mypy 2.0 in strict mode for backend type checking. Faster, more accurate alternatives have gained traction (pyright, ty, pyrefly). Worth evaluating whether to stay on mypy or move to one of them.

# Outcome

A documented decision on which Python type checker the backend uses going forward, with tooling (pre-commit, CI) updated to match.

# Acceptance criteria

- A decision is made and documented: stay on mypy, or migrate to an alternative.
- The chosen tool supports our existing stack: strict-equivalent mode, SQLAlchemy inference (plugin or built-in), async code paths, Pydantic.
- Pre-commit hook and any CI integration reflect the decision.
- Existing `app/` code passes cleanly under the chosen tool (matching today's mypy-on-`app/` clean baseline).
- Rationale (why this tool, why not the others) is captured in the issue/PR thread.