fix(api): ship web-push in the API image

The image installs only the dependencies listed in apps/api/package.json,
and web-push was added to the root one alone with push notifications, so
the API died at start with «Cannot find module 'web-push'» and its
healthcheck never passed.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

apps/api/package.json

@@ -31,6 +31,7 @@
     "rxjs": "^7.8.0",
     "tslib": "^2.8.1",
     "typeorm": "^0.3.31",
+    "web-push": "3.6.7",
     "ws": "^8.22.0"
   }
 }