Please bare with my lack of knowledge about caching methods. Can't the server check the language of the browser before rendering any page, serving the cached page corresponding to that language?

The main use case of this request is to offer first-time anonymous users content in their language when available. Asking preferences for next visits (recognizing users with cookies?) might be an improvement, but I still wonder whether the good and consistent solution is possible.

I was referring to the fact that one url equals one content. Anything else needs exceptions in frontend caching layer (or bypassing it).

Are you looking for a solution that works for Wikimedia sites, or something for other wikis? The solution for former is likely much more involved than the latter.

Third party mediawikis would be a good start, yes. I also wonder whether Wikimedia multilingual sites (my use case is mediawiki.org) have the same problems of traffic/caching than, say, the big Wikipedias.

When $wgTranslatePageTranslationULS is true, could we redirect from any visit to the canonical URL of the translatable page to the translation page for the current interface language? To allow intentional visits of other translations, perhaps an URL parameter could be added; or there might be smarter solutions.

In T110489#1621383, @Qgil wrote:

I also wonder whether Wikimedia multilingual sites (my use case is mediawiki.org) have the same problems of traffic/caching than, say, the big Wikipedias.

They have the problem that the same caching mechanism as Wikipedia's is imposed on them. :)

Serving different content at the same URL is bad most of the times anyway, users often become unable to choose what they want to see.

In T110489#1623712, @Nemo_bis wrote:

Serving different content at the same URL is bad most of the times anyway, users often become unable to choose what they want to see.

What about replacing content with translated content in-place? Something similar to how some javascript extensions work.

Since T216811: Special:MyLanguage should use browser defined language for anon users on multilingual wikis was merged into this, I would like to note that Special:MyLanguage links also do not redirect to the right pages for anonymous users. Users with accounts also rarely have the right user preferences set on the wikis that use Special:MyLanguage links, so they also get served content in English first. This should probably be fixed, especially since those links feature prominently in every wiki’s footer etc.

Anonymous users cannot set interface language on Wikimedia wikis (that is T58464: Allow anonymous users to change interface language on Wikimedia wikis with ULS).