Hello.
The calendar is not showing at the page, because you are having JavaScript errors at the page:
Error: TypeError: jQuery(...).prop is not a function
Source File: https://beyer-springeamdeister.de/wp-content/plugins/booking/js/client.js?ver=1.0
Line: 906
This issue relative to loading of jQuery library by your actual theme second time in header of your page:
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.5.1/jquery.min.js"></script>
Description about issue.
Your actual WordPress theme is loading of jQuery library in not correct way, relative to WordPress standards.
Please read more info exist here https://wpbookingcalendar.com/faq/loading-jquery-twice/
How to resolve this issue?
You can activate default WordPress theme and then you have to see that the calendar will be visible.
1) You can remove (or comment) loading of jQuery (this code)
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.5.1/jquery.min.js"></script>
from the header.php or functions.php of your actual theme. Please Open the WordPress > Appearance > Edit menu page, then select previous file(s) and search for the code, from above description.
2) Or you can contact the support of this theme about fixing issue of loading jQuery library relative to the WordPress standards (with dependence) and not directly as its right now.
Kind Regards.
