Good evening Johannes and welcome back!
Thank you for reaching out to us.
We are sorry to hear about the issues you are encountering while trying to display Google maps.
I would love to help you with this topic.
Full disclosure, certain web hosts will force the use of their Google Map API, resulting in the daily limit being reached quite often. Hopefully, this is not your case.
To answer your question and hopefully solve the issue completely for you, I would recommend reading the following very carefully: https://theeventscalendar.com/knowledgebase/setting-up-your-google-maps-api-key/
Let me know how that goes.
Best regards,
Geoff B.