feat: migrate backend persistence from TinyDB to MongoDB Atlas

- Implement lazy MongoDB client initialization in backend/db/mongo_client.py.
- Create Gunicorn configuration to ensure MongoDB client is initialized per worker.
- Refactor database access layer to support MongoDB with a new MongoLockedTable adapter.
- Add migration script to transfer existing TinyDB data to MongoDB, preserving idempotency.
- Update tracking event handling to ensure deterministic ordering with a monotonic sequence.
- Modify tests to use mongomock for MongoDB integration and ensure existing tests pass.
- Add integration test script to run tests against a local MongoDB Docker container.
- Document environment variables and migration process in specs/feat-database-migration.md.

backend/gunicorn.conf.py

@@ -0,0 +1,17 @@
+"""Gunicorn configuration for the chore/reward Flask backend.
+
+This file is automatically loaded by Gunicorn when it is started from the
+backend directory.  It ensures each worker process creates its own MongoDB
+client after forking, avoiding shared socket/file-descriptor issues.
+"""
+
+
+def post_fork(server, worker):
+    """Reinitialize the MongoDB client in each worker process after forking."""
+    try:
+        from db.mongo_client import init_mongo_client
+        init_mongo_client()
+    except Exception:
+        # If MongoDB is not configured (USE_MONGODB=false), there is no client
+        # to initialize; ignore the error silently.
+        pass