Hi,
hosting provider says, there is no aggressive caching installed. And that it is not possible to flush the cache in general.
And I know, that it is wierd, that is why I ask you.

No further ideas? I mean, it seems I am not alone here with the problem.
Meanwhile I will switch the menü on desktop to the normal menu, so peaple can reach the content.
In case you will work on the problem, you might switch that back to burger menu for the time you work on it and after that switch it back as you found it.

Thanks for a shorttime-answer!