Fix auth bypasses, race condition, stale connections, and unbounded query

- Block disabled accounts at login and unimpersonate (C4, C2)
- Catch IntegrityError on register commit to return 409 instead of 500 (C5)
- Stop _seed_admin from overwriting existing admin password on restart (C8)
- Cap public/stats query at 500 users to bound memory usage (C3)
- Rate-limit PUT /me/password at 5/minute (C6)
- Bump SQLAlchemy to 2.0.50 and aiomysql to 0.3.2; re-enable pool_pre_ping (C7)

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

backend/app/database.py

@@ -4,7 +4,7 @@ from sqlalchemy.orm import DeclarativeBase
 from app.config import settings
 
 
-engine = create_async_engine(settings.database_url, echo=False, pool_recycle=1800)
+engine = create_async_engine(settings.database_url, echo=False, pool_pre_ping=True, pool_recycle=1800)
 AsyncSessionLocal = async_sessionmaker(engine, expire_on_commit=False)