As per the screen shot ,you are part of PIadmin and PIWorld. Would request you to add everyone account in PIWorld identity and test if it is working. You may need to restart PI Web API if changes are not picked immediately.
Are you using delegation i.e. using service account on app pools? Also would request you to check PI Security i.e. access to PI and PI Vision. Please check app pool settings and web api settings for the same.
Recommend to check below blog by Eduardo on PI vision security :
thank you for your replay.
I´m using Kerberos Delegation. This is working though This is already working thouout the IIS - as you can see on the screenshot from Data Archive. I´m also able to connect to Data Archive via SMT on the PI Vision Server. I´m able to see all TAGs and everything else I usually see on SMT. PI Web API is able to crawl the Data Archive and is using the same useraccount as PI Vision. That is strange for me.