The file id_ecdsa.pub must be transferred to the remote host. For this we can use ssh-copy-id:
$ ssh-copy-id -i ~/.ssh/id_ecdsa.pub username@remote-host
This may produce the following message:
/usr/bin/ssh-copy-id: INFO: Source of key(s) to be installed: "/home/username/.ssh/id_rsa.pub" The authenticity of host 'remote-host (188.8.131.52)' can't be established. ECDSA key fingerprint is SHA256:tygMarTe3SOjTcY9HzldKThxQzsTeiYHg5JmjB2bxeg. Are you sure you want to continue connecting (yes/no)? yes
Having confirmed the access key to remote-host, the copy operation will commence:
/usr/bin/ssh-copy-id: INFO: attempting to log in with the new key(s), to filter out any that are already installed /usr/bin/ssh-copy-id: INFO: 1 key(s) remain to be installed -- if you are prompted now it is to install the new keys username@remote-host's password: One-time password (OATH) for `username`:
Type your password (and the 2FA passcode) to actually start the file copy.
Number of key(s) added: 1 Now try logging into the machine, with: "ssh 'username@remote-host'" and check to make sure that only the key(s) you wanted were added.
The passwordless/2fa codeless ssh login is now in place.