Syncing doesnt work despite having a public profile

This happens occasionally, just give it some time and it will fix itself

If you search the discussions for the word "sync", there are a lot of other threads about the same issue and it doesn't seem like there is a solution other than just trying once in a while until it works. It is probably an issue with Steam.

Try changing to private. Sync, then back to public and sync. That worked for me when it was failing. It may not work but its worth a try.

Mine just spontaneously resolved itself.