authelia: HTTP Basic Auth not working as expected for nginx-ingress / kubernetes

Authelia is used inside kubernetes to protecd some services used by endusers with browser. Its working nice.

Additional some technical services has to be protected. At this time these are protected by http basic auth. Ingress looks like https://kubernetes.github.io/ingress-nginx/examples/auth/basic/

Watch at curl resonse: WWW-Authenticate: Basic realm="Authentication Required - foo"

Now I want to replace this with an authelia basic auth protection like https://kubernetes.github.io/ingress-nginx/examples/auth/external-auth/

My curl response does not contain WWW-Authenticate so that the browser never shows up the login popup.

Second step is more technial and i may not understand it completley. If i authorize mysqlf with curl https://domain.tld" -u "user:pass" the information abaout the user does not show up in authelia logs.

At this point i would like to see an example how to paramterize nginx-ingress to put the basic auth credentials into the right header and format.