feat: update frontend path to '/badge' and adjust related documentation

ai-prompts/01-backend-plan.md

@@ -138,7 +138,7 @@ backend-mock/
 ### Via Script (consigliato)
 
 ```bash
-./dev.sh server           # Avvia server con frontend
+./dev.sh server           # Avvia server con frontend su /badge
 ./dev.sh server -p 9000   # Porta custom
 ./dev.sh backend          # Solo API, no frontend
 ```