Windows 10 setup now requires you to set up a PIN code when you agree with their advice to use a Microsoft Account. Therefore, when RDP tries to authenticate, it can't use the Microsoft Account password as the login is configured to use a PIN. (and using the PIN doesn't work, either, as it's not a real password on the account).
I went to the host PC (to which I want to RDP), locked the console via ctrl-alt-del, unlocked it with my Microsoft Account password instead of the PIN. Then, back on the RDP client PC, I was able to complete the connection using the Microsoft Account password.