Can't sync on steamgifts, profile is set to public, games public etc. Although I probably know why

The not being able to sync has been an issue for quite a while, definitely doesn't have anything to do with the Steam UI change.
If I can't sync, I simply switch my Steam profile to private and back to public and syncing works again.

SG uses the Steam web API to sync and not the client.
Hopanda's solution usually works for me.

The new Humble Monthly Choice has just arrived and many users are currently using Steamgifts to create new giveaways (or to enter these giveaways). Your sync problem is probably just due to some sort of traffic jam. I think it will get better in a few hours when Steamgifts will be less used.

Edit: Otherwise you can also try to sync regularly (like every 3 min) because it can sometimes succeed after several attempts when the site is so busy (it's just a matter of luck).