Thanks Brad for the implementation explanatin but I'd rather need a document outlining the expectations for user-facing functionality.
I just had to separately and manually login three times (on Meta, then on Wikipedia, then on MediaWiki.org) in order to be logged in on most wikis. I don't find any page explaining whether it's normal for global login to require entering my password 3+ times. If it's expected and documented, I can stop worrying.
Nemo