Can I have a duplicator copy of your site as when I try to edit the problematic archive page it shows 501 server error with the "aktivitaeten" archive.
Also - we do not recommond to debug/troubleshoot on live/production sites.
The Archive "Presseberichte" has got the same problem but in the backend it is editable without error. So perhaps you can work on this archive to find the problem.
The link you shared to download the All in one WP migration package is too big almost 7-8GB.
Can you try to build the package by excluding the media when you build the package or just grant me permission to take copy of your site and I will do it.
I have set the next reply to private which means only you and I have access to it.