This thread is resolved. Here is a description of the problem and solution.
Problem: When I publish the product in English, the Greek version does not get published. When I go to the Greek version of the product to publish it (make it public) manually, the option is locked and it remains private.
Solution: I'm afraid that this is in fact a known bug of WPML (it also happens with posts). As a workaround you could:
1- Go to WooCommerce>WooCommerce Multilingual>Products
2- Click the pencil icon to edit the translation of your product (the one with incorrect visibility status)
3- Mark the translation as finished and save it
Once done, the visibility status should be synchronized with the original product.
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