Add REGISTRY_PUBLIC_URL for UI quick-start and proxy setups.

Dashboard and guide now show the configured registry host instead of deriving it from the UI hostname.

Co-authored-by: Cursor <cursoragent@cursor.com>

.env.example

@@ -1,7 +1,12 @@
 # Public URL that docker clients use to reach the Nuxt auth endpoint
-# Behind NPM/Traefik this should be the HTTPS URL, e.g. https://registry-ui.example.com
+# Behind NPM/Traefik this should be the HTTPS URL of the admin UI
 AUTH_PUBLIC_URL=http://localhost:3080
 
+# Public registry host shown in UI quick-start / used by docker login·push·pull
+# Local: localhost:5050
+# Behind proxy: docker.sejong.dev  (or https://docker.sejong.dev — scheme is stripped for CLI)
+REGISTRY_PUBLIC_URL=localhost:5050
+
 # Registry token auth (must match auth.token.service / issuer in registry config)
 REGISTRY_AUTH_SERVICE=registry
 REGISTRY_AUTH_ISSUER=registry-aio