Until late last year I could access my Home-Assistant via VPN with the iOS app per mobile data and external WiFi. Both does not work at the moment. A WiFi VPN connection works only from the same WiFi net where the Home-Assistant is located.
Error Message : NSURLErrorDomain -1009 - The Internet connection appears to be offline.
Accessing Home-Assistant via VPN and Browser works.
What changed ? What needs to be done to get it working again with the iOS-App over VPN ?
The error is an iOS error and have nothing to do with HA as such.
Your phone is not able to make the connection at all to the address.
There have been a few posts on this earlier and in some of the cases it has been the ISPs malware filter that have blocked connections to duckDNS domains. I think it was O2 in the UK last time, but many ISPs use a malware filter and do not have it managed properly.