Investigate ty type checker alongside mypy

Summary

ty is Astral's Rust-based Python type checker (beta). It's 10-100x faster than mypy, checks unannotated function bodies by default, and supports advanced features like intersection types and reachability analysis.

libtmux is well-positioned for ty adoption:

• No mypy plugins in use (ty's biggest gap — no plugin system)
• Only 9 type: ignore comments across the codebase
• Already uses Astral's ruff and uv tooling
• Strict mypy configuration with full type annotations

Goals

1. Add ty as a dev dependency alongside mypy (not replacing it)
2. Add ty configuration in pyproject.toml and justfile targets
3. Add ty to CI as a non-blocking step
4. Compare diagnostics: what ty catches vs mypy, false positives, speed
5. Determine if ty can eventually displace mypy

Approach

• Gradual adoption: run both checkers in parallel
• Start with known-noisy rules suppressed, re-enable incrementally
• CI runs ty with continue-on-error: true so it doesn't block builds
• Document findings in the PR for future reference

References

• ty documentation
• ty rules reference
• Migration guide: mypy to ty

Start by reviewing pyproject.toml, the justfile, and the repository's CI configuration, then read the ty documentation and run ty alongside mypy. Add the development dependency, configuration, targets, and non-blocking CI step described in the issue. Done means both checkers run, diagnostics and speed differences are documented, and the CI step does not block builds.