Tested on Chrome and Firefox (both desktop, not tested on mobile so far...) and two different computers:
Logged in using the desktop site of some wiki.
Visit http://commons.m.wikimedia.org, and get a login toast notification with message "Central login
You are centrally logged in. Reload the page to apply your user settings."
If i reload the page, i get the same toast again (and on every other page view).
Maybe related to T88860: Authentication sharing between desktop and mobile Commons is broken ?