Document task DB access and unify background task DB handling

backend/app/tasks/db.py

@@ -0,0 +1,29 @@
+"""Shared database helpers for APScheduler background tasks."""
+
+from __future__ import annotations
+
+from contextlib import asynccontextmanager
+from typing import TYPE_CHECKING
+
+from app.db import open_db
+
+if TYPE_CHECKING:
+    from collections.abc import AsyncIterator
+
+    import aiosqlite
+
+    from app.config import Settings
+
+
+@asynccontextmanager
+async def task_db(settings: Settings) -> AsyncIterator[aiosqlite.Connection]:
+    """Open a dedicated application database connection for a background task.
+
+    Background tasks run outside FastAPI request scope and therefore must
+    manage their own SQLite connection instead of using FastAPI dependencies.
+    """
+    db = await open_db(settings.database_path)
+    try:
+        yield db
+    finally:
+        await db.close()