Hi Christos,
Thanks for getting in touch with us.
It is on purpose and that is okay.
Officially, the sitelinks searchbox code only needs to appear on your homepage:
https://developers.google.com/search/docs/data-types/sitelinks-searchbox
Add this markup only to the homepage, not to any other pages.
Hope that helps and please do not hesitate to let us know if you need our assistance with anything else.
Hello,
Since we did not hear back from you for 15 days, we are assuming that you found the solution. We are closing this support ticket.
If you still need assistance or any other help, please feel free to open a new support ticket, and we will be more than happy to assist.
Thank you.