Refactor database connection handling in API endpoints

- Removed direct pool checks and replaced them with a centralized database initialization method in `init_db`.
- Updated API endpoints in `admin.py`, `collection.py`, `pins.py`, and `watched.py` to ensure the database connection pool is initialized before usage.
- Enhanced error handling to raise HTTP exceptions if the database is unavailable.
- Improved the `init_db` function in `database.py` to prevent multiple simultaneous initializations using an asyncio lock.

backend/app/api/admin.py

@@ -1,7 +1,6 @@
 """Admin API endpoints"""
 from fastapi import APIRouter, HTTPException, Header
 from typing import Optional
-from app.core.database import pool
 from app.core.config import settings
 from app.services.sync import sync_all_arrs