Oh, thanks for reminding me of this issue! I have already solved the problem myself. I had the plugin “Captcha für Contact Form 7, Avada, Elementor und WordPress” (by Forge12) installed, and I think this caused the problem. After deactivating the captcha, the form could be sent without any problems.
I now use another captcha (by Cloudflare Turnstyle) and this works just fine ??