Migrate pre-commit hooks from pre-commit to prek

Replace the Python-based pre-commit framework with prek (Rust) for
faster hook execution. Convert .pre-commit-config.yaml to prek.toml,
remove pre-commit from dev dependencies, and apply ruff auto-fixes
(UP037: remove unnecessary string quotes in type annotations).

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

CLAUDE.md

@@ -10,9 +10,9 @@
 
 # Pre-commit Hooks
 
-This project uses [pre-commit](https://pre-commit.com/) to run linting and formatting checks before each commit.
+This project uses [prek](https://prek.j178.dev/) (Rust-based pre-commit framework) to run linting and formatting checks before each commit.
 
-**Setup:** `pip install pre-commit && pre-commit install`
+**Setup:** `prek install`
 
 **Hooks configured:**
 - **Backend:** `ruff check --fix` and `ruff format` on Python files under `backend/`