There is no way to access the image on Commons from the website without being logged in.
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The issue, if I'm understanding this correctly, is that clicking on the the image at https://office.wikimedia.org/wiki/Main_Page brings up https://office.wikimedia.org/wiki/File:Wikimedia_Foundation_All_Hands_2018_-_Myleen_Hollero_(edited).jpg, which isn't available to non-users
Solution: add that page to wgWhitelistRead
Is there someone who needs to approve this for the office site?
I don't think so, I think you can treat this as any other site configuration change.
For what it's worth, I agree that this is a good idea.
The error "page" is actually https://office.wikimedia.org/wiki/Main_Page#/media/File:Wikimedia_Foundation_All_Hands_2018_-_Myleen_Hollero_(edited).jpg, which is failing due to the underlying https://office.wikimedia.org/w/api.php?action=query&format=json&prop=imageinfo&titles=File%3AWikimedia_Foundation_All_Hands_2018_-_Myleen_Hollero_(edited)%2Ejpg&iiprop=url&iiurlwidth=1024&smaxage=86400&maxage=86400 erroring with:
code: readapidenied
info: You need read permission to use this module.
Probably needs whitelisting https://office.wikimedia.org/wiki/File:Wikimedia_Foundation_All_Hands_2018_-_Myleen_Hollero_(edited).jpg AND disabling the Media Viewer setting by default on officewiki, so that anonymous users don't use it.
Hmm at this point it might be easier to edit the page to avoid this.
We could replace the image:
[[File:Wikimedia Foundation All Hands 2018 - Myleen Hollero (edited).jpg|right|frameless|500px]]
…with:
<div class="noviewer">[[File:Wikimedia Foundation All Hands 2018 - Myleen Hollero (edited).jpg|link=commons:File:Wikimedia Foundation All Hands 2018 - Myleen Hollero (edited).jpg|right|frameless|500px]]</div>
The class="noviewer" disables MultimediaViewer, and link=... links directly to Commons instead of the inaccessible local image page.
We'll need an Officewiki administrator to edit the page. @Reedy?
FWIW the div is unnecessary, MediaViewer does not open images which link to a non-standard URL (since these are usually used for navigation).