We are currently located in Austria.
I have also tried pinging via external servers, and the host DNS may not be registered yet globally. Only some of the locations respond to pings: https://i.imgur.com/TzHYzCA.png
I added the IP to our local hosts file, and then I was able to access the site.
I also found the cause of the issue. In the search.php template file in your theme directory, there were two additional query sections – I assume one is for some sort of featured posts, the other is for the search results. However both are triggered as search queries, so the plugin has no way to decide which one to override the results for.
To resolve this, I made a copy of that file in you child template directory and added this line to the feature query: https://i.imgur.com/UBDUVr5.png
That will excplicitly declare the query not to be touched by ajax search pro.
