I'm re-opening this, because I believe it is a different feature-request from that given in T111913: [Story] In the "other projects" sidebar on multilingual wikis, link to wikis in the user language.

This task is asking to solve the use-case of:

• As a user at [language-specific project, e.g. French Wikipedia], with my language-preference set to the local language, and looking at the Main Page (e.g. w:fr:Accueil_principal)
• When I click on the link to Commons or MediaWiki in the "In other projects" section of the sidebar
• I expect to be taken to https://commons.wikimedia.org/wiki/Accueil and to https://www.mediawiki.org/wiki/Special:MyLanguage/MediaWiki (note that Special:MyLanguage/ doesn't work as expected on Commons)
• But it currently sends me to the English version

Whereas the other task is asking:

• As a user already at a multilingual wiki (e.g. Commons)
• When I click on the link to a language-specific project (e.g. Wikipedia)
• I expect to be taken to [the language edition that is set in my local/global preferences]
• But it currently either:
  • doesn't have most of the projects listed (see e.g. https://species.wikimedia.org/wiki/Accueil )
  • or goes to the English version

IIUC (Iamnotadev!), both problems are essentially caused:

1. because (e.g.) https://www.wikidata.org/wiki/Q21445585 ( French main page of a multilingual-project) is distinct from https://www.wikidata.org/wiki/Q5296 (Wikimedia Project Main Page),
2. and possibly because some of the multilingual projects currently use different translation systems (i.e. Extension:Translate (used at Wikidata) --versus-- manually-created-&-synced-pages/subpages (used at Commons & Wikispecies))

but the tasks are asking for different things, so either they need to be mentioned in the same task description, or in two different tasks.

p.s. This feature was recently requested at https://meta.wikimedia.org/w/index.php?title=Tech&oldid=19140806#Changing_the_sidebar_%22In_other_projects%22_links