It appears to no longer be possible to override the automatically retrieved link to Pagagist with |composer=mediawiki/extension as I tried with this diff. As a result, the broken link is still shown.
Topic on Template talk:Extension
It turned out that the link I tried to add was a link to some outdated extension fork. However, this brings me to the next issue. There is a link to Packagist even though the extension is not listed on Packagist. Obviously, not every extension with a composer.json file can be installed with Composer. How do I remove the link from the info box?
Since the information about Packagist is set in the composer.json file on the repository, you'll have to submit a patch and change it to the correct name. Then it will be updated automatically on this page once merged.
@Kghbln: The name in that extension's composer.json is mediawiki/openidconnect (i.e. without hyphens), but yeah it's also not registered with Packagist. The fix is as @Ciencia Al Poder says, to remove the name from composer.json — alternately, the package could be registered on Packagist (although probably not under the mediawiki namespace, I think that's deprecated now). @Cindy.cicalese: You could register it under your own namespace on Packagist.
In the meantime, even though I am not actively looking for this, I have found another three or four extensions where none of this works, e.g., it shows a link to Packagist even though the extension is not registered there. We need either a way to disable the link to Packagist or someone should go through all repositories and fix the composer files.