Ok, back at my Air, the passkey from my mini synced over iCloud to my Air.
And I can login in with the Air over passkey.
So I deleted the passkey again.
And tried to create a new one. Which worked 
I got an 502 error the first time I clicked on “Add passkey” but it worked the second time.
So I don’t know what really caused this, maybe the update on my Air to 15.4.1.
Either way, the problem is solved for me 