chore: migrate from mypy to ty type checker

Summary

Migrate the backend type checking from mypy to ty (https://docs.astral.sh/ty/), the new type checker from Astral (creators of uv and Ruff).

Motivation

We're already using Astral tools in our stack:

• UV for package management (10-100x faster than pip)
• Ruff for linting and formatting

Adding ty would complete our migration to the Astral ecosystem, providing:

Performance

• 10x - 100x faster than mypy (benchmarks on home-assistant project)
• Built in Rust for maximum speed
• Fine-grained incremental analysis optimized for IDE workflows

Better Developer Experience

• Full language server with code navigation, completions, inlay hints, and auto-import
• Configurable diagnostics with per-file overrides
• Better support for partially typed code and gradual adoption
• Advanced type narrowing and reachability analysis

Ecosystem Consistency

• Same configuration style as Ruff (pyproject.toml)
• Unified tooling from one vendor
• Simpler CI/CD configuration

Tasks

• [ ] Add ty to dev dependencies (uv add --dev ty)
• [ ] Configure ty in pyproject.toml
• [ ] Update CI workflow (.github/workflows/ci.yml) to use ty instead of mypy
• [ ] Update CLAUDE.md documentation
• [ ] Update Makefile commands
• [ ] Remove mypy from dependencies
• [ ] Fix any new type errors ty may catch (ty may be stricter in some areas)

References

• ty documentation: https://docs.astral.sh/ty/
• ty GitHub: https://github.com/astral-sh/ty
• Astral blog announcement: https://astral.sh/blog/ty

Notes

⚠️ ty is relatively new - we should verify it's stable enough for production use before migrating. Consider testing on a feature branch first.

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