I have dealt intensively with the problem over the weekend - unfortunately without a satisfactory solution.
It must have something to do with the DNS resolution, but what exactly I can not explain.
If I change the IP address from Static to DHCP and restart unRaid, I have an internet connection including correct DNS resolution. If I change the IP back to Static, I have after a reboot again no DNS resolution (ping on 8.8.8.8 still works fine).
It is interesting that the values of the DNS servers are identical with DHCP as well as with Static.
It is to despair. Since I can't rule out a LAN problem 100%, the problem search will probably continue for a while.
I will, if I find time, report again this week.