Either something is not properly configured on my side or i have another understanding ot the path attribute:
    "url": "http://localhost:8080/schulen/primar-wolfhausen/schulportrait/",
    "api_endpoint": "http://localhost:8080/api/cms/de/pages/schulen/primar-wolfhausen/schulportrait/",
    "path": "/api/cms/de/pages/schulen/primar-wolfhausen/schulportrait/",In my opinion, it should return
    "url": "http://localhost:8080/schulen/primar-wolfhausen/schulportrait/",
    "api_endpoint": "http://localhost:8080/api/cms/de/pages/schulen/primar-wolfhausen/schulportrait/",
    "path": "schulen/primar-wolfhausen/schulportrait",basically the attribute for path should be similar to pages return
curl -X 'GET' \
  'http://localhost:8080/api/cms/de/menu/' \
  -H 'accept: application/json'