Backend: Implement Pyright type-checking #1119

Is your feature request related to a problem?
The backend has no type-checking command or pyright configuration. Type errors — wrong annotations, missing None guards, SQLModel/crud type mismatches — go uncaught until runtime or review. There is no consistent, repeatable way for developers (or agents) to type-check the files they change before opening a PR.

Describe the solution you'd like

• A pyright-based type-check script that runs against app/, with the option to narrow to specific paths/files.
• Pyright run in an ephemeral environment so it never mutates uv.lock.
• A shared [tool.pyright] config in backend/pyproject.toml (include app, standard mode, resolve deps from the local .venv).
• A /typecheck command that runs the script, groups errors by file, and separates real type bugs from third-party stub noise — without auto-editing code.
• The senior-engineer agent type-checks changed files before finishing, especially when app/models/ is touched.