500 error only in privacy mode (chrome)

We have a NSS 5.2.3 (Docker Container) running in our kubernetes behind traefik with a certificate by lets encrypt.

We are testing the chess app (https://pheyvaer.github.io/solid-chess/) and it's working for a normal chrome session.

But in privacy mode or in Chromium, we will got the following error for the GET request https://localhost/inbox/ with status 500:
request to https://localhost/.well-known/openid-configuration failed, reason: unable to verify the first certificate

We tested also against inrupt.net and there is no problem.

We compared the requests and found out, that the cookie nssidp.sid is missing.

We tried some startup parameters, but with no effect.

We think that is not a specific NSS issue more like general purpose for proxying or security measures.

Beginne damit, die GET-Anfrage an https://localhost/inbox/ im Datenschutzmodus von Chrome oder in Chromium zu reproduzieren, und vergleiche sie mit einer normalen Sitzung. Verfolge den Fehler bei der Zertifikatsprüfung für /.well-known/openid-configuration und das fehlende nssidp.sid-Cookie über NSS, Docker, Kubernetes und Traefik hinweg; abgeschlossen ist die Aufgabe, wenn die Anfrage ohne den 500-Fehler erfolgreich ist.