By testing on a local server I found out, that switching to another template will not actually produce this misbehaviour. Though I did not find out why becauce using a nearly empty template without any plugins (or similar) will not work.
Nevertheless we will not switch to version 4 anyway because there is no longer a backend editing function. This is neccessary for external widgets because they are not showing up in frontend editing.
So this post is just for information purposes, maybe it can help others.
Nonetheless thanks for your support.