In particular, the text that is in the mockup doesn't seem to come from
anywhere API-accessible, so we would either need to add another field to
the siteinfo API ("subtitle for this wiki on remote sites using it as a
repository for images..." verbose) or hard-code it in for Commons (see
above), which both sound unappealing.

Isn’t it possible to use <Shared-repo-name-shared> (the way <Sharedupload-desc-here> does)?

<https://www.mediawiki.org/wiki/MediaWiki:Shared-repo-name-shared>
<https://www.mediawiki.org/wiki/MediaWiki:Sharedupload-desc-here>

--
Jean-Frédéric