fix(frontend): prefix auth API requests with VITE_PUBLIC_APP_URL for cross-origin Workers hosting

.github/instructions/TODO.md

@@ -2,6 +2,11 @@
 
 > Completed tasks moved to [DONE](./DONE.md). Remaining tasks in [BACKLOG](./BACKLOG.md).
 
+## Cloudflare Workers
+
+- [x] Adjust `frontend/src/main.ts` to use `VITE_PUBLIC_APP_URL` for API requests instead of hardcoded `/api/...` paths.
+- [x] Adjust `frontend/src/main.ts` to use `VITE_PUBLIC_WS_URL` for WebSocket connections instead of hardcoded `wss://...` paths.
+
 ## Frontend Tests
 
 ### User Frontend