I think there is something different. I did not want to switch the production site to another template at a first step. This would break it for the users.
So I tried to reproduce the issue on our test site test.ulc-moedling.at. I created a new article, waited for some minuted and successfully saved it there. I noticed to see Googe reCAPTCHA there. So I checked CAPTCHA plugins: Our test site was still on old reCAPTCHA, while our production site is using invisible reCAPTCHA plugin.
Hence I switched our test site to invisoble CAPTCHA, too, created an article, waited for some minutes and it failed to save there, too.
So it has something to do with the "CAPTCHA - Invisible reCAPTCHA" plugin. I disabled CAPTCHA in the content options ("CAPTCHA Onsubmit"), because we only allow some registered members to create articles. Saving of articles is now possible either on test site as well as on production site.
I did not find out what's wrong with invisible reCAPTCHA during article creation until now.