Fix: Harden V3 search logic and restore specialized business mapping

- API: Updated `search_ae_obj_v3` to correctly serialize complex URL parameters (JSON).
- Events: Restored "sacred" business logic for Event Badge and Session searches using `ft_qry` and `lk_qry`.
- PWA: Fixed manifest path in `app.html` to resolve 404 errors.
- Documentation: Updated `GEMINI.md` and `TODO.md` with recent search hardening accomplishments.

src/service-worker.js

@@ -74,4 +74,4 @@ self.addEventListener('fetch', (event) => {
 	}
 
 	event.respondWith(respond());
-});
+});