Thanks for the detailed response. I verified the steps and do not hold any corporate managed accounts. So, apparently, it started working, but from time to time. I noticed that now my devices appear with both, my icloud account picture, and with no picture, as if I were a third party. So, with the third party options, it works now, but not when I click on the option with my icloud account (which is the same in all my devices).
The chosen setting for airdrop is all, otherwise, despite seeing my devices as contacts, they do not "talk to each other"
Maybe it's a bug? It used to work before...
At least now it's working, although some times only.