Multilangual sites - how to link pages as an language version

nr This is something that our product does, and it is a bit of tricky work with 4 hidden columns on the original page and the new one, so I am trying to think of an out-of-the-box way of doing it.

In theory if you overwrite the "translated" (copied) page that the multilingual feature creates with your own page of the same name in the same folder, and the original doesn't have those fields, then the copy will keep the original correct value.

Copying pages from one site to another is a little tricky for modern pages, I recommend using this Power Automate technique.
https://techcommunity.microsoft.com/t5/sharepoint/copy-or-move-site-page-from-one-site-to-another/m-p/255703?lightbox-message-images-836161=130041i86E9F2D2352F5F28

I haven't tried it, let me know if it works.