fix(settings): properly save and clear configuration values

Backend:
- Replace dict mutation with dict replacement to fix SQLAlchemy JSON
  mutation tracking issue (config.config = {**config.config, **update_data})

Frontend:
- Send explicit null values instead of undefined so fields can be cleared
- Update UserConfigUpdate interface to accept null values

apps/api/src/api/user_config.py

@@ -112,7 +112,8 @@ async def update_user_config(
     # Merge updates
     update_data = data.model_dump(exclude_unset=True)
     logger.info("Updating user config for user %s: %s", user_id, update_data)
-    config.config.update(update_data)
+    # SQLAlchemy JSON doesn't track dict mutations, so we replace the whole dict
+    config.config = {**config.config, **update_data}
 
     await session.commit()
     await session.refresh(config)