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>

backend/pyproject.toml

@@ -19,7 +19,7 @@ dependencies = [
 dev = [
     "ruff==0.15.0",
     "ty==0.0.17",
-    "pre-commit==4.5.1",
+
     "pytest==9.0.2",
     "pytest-asyncio==1.3.0",
     "httpx==0.28.1",