That should not be the business of the site, but of the browser. It is precisely what Accept-Language is for. The site should respect the header, allowing circumvention should be a very low accessibility priority.

The site should respect explicit user actions. A get request to a /en/ domain, or a button click to a language icon should result changing to that language. Respecting implicit preferences that are more likely than not be just plain wrong anyways should be a very low priority, ideally shouldn't be done at all.

The browser just looks at the system language. That may be US English, but you want to read the site in Spanish for example.

It defaults to it, but the preferred language can be changed in all major browsers, though currently not on a per-website basis.

I am using Chrome and I have no idea how to change the browser language. I mean, I could probably find out.. digging into Preferences.

That's a silly solution in any case, since you literally use the browser for other sites. Dozens of tabs.

Which browser, if any, even allows you to modify this header per-website?

One example is qutebrowser:

https://qutebrowser.org/doc/help/settings.html#content.heade...

I assume other developer-centric browsers have similar options.

Firefox with this addon: https://addons.mozilla.org/en-US/firefox/addon/accept-langua...