PS: The ContentTranslation extension have some sort of similar function - when you click on a link, you get the link in your own language if exist, and as a fallback the link in the source language.

@eranroz Could you please add an example page? Do you mean we should do this for links from hewiki to enwiki (for example)?

Here is a motivating example with mock screenshot:
Supposed I'm farsi speaker looking for "K-means" article. Since K-means doesn't exist in fawiki, I'm going to enwiki https://en.wikipedia.org/wiki/K-means_clustering
While reading the article I encounter a term "cluster analysis" which I would like to get its summary - preferably in farsi so I'm moving the mouse over the link and Popup with Farsi content appears rather then enwiki.

Mockup (for https://en.wikipedia.org/wiki/K-means_clustering?uselang=fa):

Thanks for the explanation @eranroz!

I see, so this would need cross-wiki uploads and then switching wikis based on user languages. Is that right?

I am not sure if this is the experience the user would expect. The user is only setting the UI language, getting content from a different wiki because of this setting might not be a good idea.

Or are you saying that the content of enwiki should be machine translated and shown? That would still mean that we are changing content language based on the UI language setting.