It looks like extension MediaWikiAuth is the older extension which provided OAuth, initially written by @ashley.
https://www.mediawiki.org/wiki/Extension:MediaWikiAuth
There are lots of wikis which use it
https://wikiapiary.com/wiki/Extension:MediaWikiAuth
We should attempt to support these wikis also.
@jayvdb, according to the description of MediaWikiAuth, I think it's used as an extension for a wiki site which wants to import user accounts from another wiki site. It's not like an OAuth extension in my opinion.
MediaWikiAuth is a hacky extension for MediaWiki that silently imports accounts from other wikis. There should be nothing that Pywikibot needs to do specially to support it.
Some other extensions which might be worth looking at:
https://wikiapiary.com/wiki/Extension:SocialLogin
https://wikiapiary.com/wiki/Extension:TwitterLogin
https://wikiapiary.com/wiki/Extension:GoogleLogin
There's a large re-write of the whole authentication layer coming soon (https://gerrit.wikimedia.org/r/#/c/195297/) so I'm not sure if it makes sense to invest a lot of time supporting various extensions when we should soon (I hope!) have a standardized way of doing it.