Hi Valentin,
I am travelling a lot this week, so I won’t have much time, but I can try to do some tests. What WooCommerce version, WordPress version, plugin version are you using?
Enable WordPress debug mode on your site. Here is a list of tutorials for you: https://conschneider.de/troubleshooting-skills-using-debug-mode/ – afterwards please try again and check whether your log file has any records. If there are, please post them here.
Also a conflict check can never hurt. You can use https://www.ads-software.com/plugins/health-check/ for this. It allows you to deactivate all plugins and activate a default theme just for your user session. Here is a quick tutorial: https://conschneider.de/check-conflict-wordpress-fast/
**Before you do that, please do make a full backup!**
Here are some tips on how to do so: https://conschneider.de/how-to-backup-your-wordpress-database-and-files/
Kind regards,