Thank you very much for the proper details, it made my work much easier. I've looked at the issue directly via FTP, but somehow the WPML translation returns the incorrect post type slug. I have tried to look on the WPML forums and their support page to see if this is a known issue, or if there is any solution to initialize the slug translation, but I have not found anything.
I have solved the issue with a custom code, that I placed in the child theme directory, into the functions.php file. The links should be correct now.
For future reference, the code is:Best,
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