feat(worker): adopt canonical public URL

docs/implementation-roadmap.md

@@ -30,8 +30,10 @@ Worker repository:
 
 - wire local inventory and metrics collector lifecycle into web server start
   and shutdown;
-- validate full HTTP config, including the accepted `PUBLIC_URL`, in main
-  startup;
+- [x] validate full HTTP config, including the accepted `PUBLIC_URL`, in main
+  startup (milestone 1 of
+  [public-endpoint-and-identity.md](public-endpoint-and-identity.md): origin
+  shape, production HTTPS, legacy `WORKER_URL` fallback);
 - [x] reconnect in memory on token rotation without stopping the runner;
 - [x] resend bounded check/notification results after websocket reconnect;
 - define process policy when the web listener exits unexpectedly;