Good evening Andrei,
Thank you for the screenshot.
Try adding the following CSS rule to your style.css file or in your Custom CSS metabox:
.datepicker-dropdown {z-index: 999 !important}
If that does not work.
Could you please send me a copy of the latest version of your WordPress theme / child theme via a link to a .zip file link (stored Dropbox or Google Drive) so that I can run some tests on my end ? I recommend a private reply for that purpose.
Please ensure you are using the latest files as found on your actual website.
This way I will get access to any updates or customizations you might have made.
Let me know how that goes.
Best regards,
Geoff B.