I went to https://wikipedialibrary.wmflabs.org/ and clicked the "Log in" button. It then took me to Meta to authenticate.
At https://meta.wikimedia.org/w/index.php?title=Special:OAuth/authenticate it gave me the following error and left me there instead of returning to the Wikipedia Library:

Application Connection Error
This request has already been completed and cannot be resubmitted. Go back to the application and try to connect your account again, or contact the application author.
OAuth token already used, E009

I manually returned to the Wikipedia Library and clicked the "Log in" button again. This time, it authenticated successfully without taking me to Meta.