Hey Jan,
Sorry you’re having trouble here, I’m happy to help and try to sort things out. You mention these things in your post:
Have downloaded the zip file from my account / Download
Have checked the lic key
What happens, specifically, when you try to update the plugin manually? If you cannot run the update successfully, then what I’d recommend doing is a “clean install” of the 3.12.x version of Events Calendar PRO.
To do that, you essentially just first make a back-up of your site and database if possible; the following steps will not erase any data from your site, but backups are just a good precautionary measure regardless!
Then, delete – not just deactivate, but delete – the existing version of Events Calendar PRO off of your site.
Then download a fresh copy of it from theeventscalendar.com/my-account/downloads.
Finally, install this “fresh” version and activate it on your site. Proceed with entering your license key again when prompted, and you should be good to go! 🙂
Let me know if this helps!
– George