Can't reproduce here. Code implies that an associated item (here an article) has priority over a menu item.

See for example here: article in English, the Italian flag points to the Italian associated article, the English flag points to menu URL and not to current article. Same for Italian article: English flag link is ok, Italian flag not ok.
Probably because there is no associated English article to current article but... since it is the article itself?

what are the settings of this site? They look pretty weird.
I see homes do not display anything and there are no menu modules with links.

domain.info/OTHER/j4/
domain.info/OTHER/j4/it/

This does not look like a joomla issue. You should use the forums to try to solve your problem.

I put up this very simple scenario/site just for showing this issue (it is an almost empty site in a subfolder of an exiting site) but you can see the same issue in the main site, for example here

I confirm.
Is it a real issue? Not really as it is useless to click on the flag for the same language.
This is why we may set the Active Language parameter to No in the module when not using dropdown.
Nevertheless we should try to solve that.

Make the flag for the active language inactive?

We could do that, but I am looking at another possibility right now.

Semantically it probably should be disabled/inactive

Displaying the flag or language name without a link would look pretty weird.
Users may think something is wrong when they click on it.
I prepared a PR which will correct the issue and display the current url.

Just as a "home" link shouldnt be enabled on the home page

Not related at all.
The home link IS enabled. The only difference is that it does not need associations to be associated.
The link in that case is simply
$language->link = JRoute::_('index.php?lang=' . $language->sef . '&Itemid=' . $itemid);

Closing as we have a patch
#22558

@Giuse69
I can add the full modified file there if you can't apply patches.