What syncs when you don't have enough iCloud storage? When you don't have enough iCloud storage (which happens, for example, when you are downgraded from a higher plan to a lower one), you aren't able to sync many iCloud items anymore because you're over your iCloud storage limit. This prevents iCloud Photo Library photos and iCloud Drive files from syncing. However, it (thankfully) doesn't seem to prevent your contacts or your calendar items from syncing across your devices.

Is there a list of what can and can't be synced when you're over your iCloud storage size?
There isn't exactly a list, but if you look at their suggests as to what to do when it is full (https://support.apple.com/HT204247), you can see the things that are affected. Other types of data are not, such as those listed in https://support.apple.com/HT202158