Like i said in my post above i have a copy of the page for testing… the orgininal page (the page i posted) has the old versions like u said…so i made a copy and upgradet every version to the newest (WordPress: Version 5.4.1 \Contact Form 7: Version 5.1.8).
At the original Version, the “succesfully sended” notification appeared but no email was send. At the updated version not even the nofication is showing, the only thing you can see after pushing the “Send”-Button is the “ajax-loader”.
If required i can send you login data for my testing page as PM.