I solved it on my side now so I will propose my solution.
I used to beta test macOS Catalina on an external SSD connected via T3 to my MacBook Pro.
Naively, I logged in with my AppleID on that account and turned on all things iCloud.
For quite understandable (now) reasons the two logins from the same machine in two different macOSs created a conflict in the sync.
I booted today from that disk, signed out from my AppleID, saving a copy of the (possibly) not uploaded things to a folder which then I emailed me, and then rebooted into my main disk with Mojave.
Headed into System Preferences > iCloud, turned Safari back on and, after a few minutes, everything started working again.
Maybe you have a similar situation, or even another machine which is just logged in with the same AppleID.
I hope this sheds some light at least.