I have to apologize. This is embarassing. I wasn’t at home when I tried the other sync tool. I was logged in via Fritz!Box VPN. All my previous attempts where made connected by local Wifi, same subnet. When I tried Calendar Sync trial at home using Wifi, it failed too. Then I tried Davdroid over VPN, and it worked.
After digging around I found the problem. I activated a safety mechanism in synology DSM long time ago when I routed Synology ports to the public internet adress. If one IP enters wrong credentials more than 3 times, it is added to a blacklist. I must have entered wrong credentials more than three times when I configured DavDroid and my mobile’s DHCP adress got blocked. As VPN users get a different, unblocked IP, it worked.
So embarassing Sorry to wast your time and of course davdroid works just fine with Synology’s WebDav-Server.
Have a nice evening.