The "Contact us" form doesn't send anything to my inbox either.
Edit got an error message now:
Swift_TransportException: Email to firstname.lastname@example.org failed: Connection could not be established with host smtp.office365.com :stream_socket_client(): unable to connect to tcp://smtp.office365.com:587 (Connection refused)
Seeing your edit, that error is well before the TLS component -- it's a network-stack-level error suggesting the connection was refused. You may need to look at your firewall/security settings for example (note that they may differ depending on the Linux user that's triggering the action). This can include SELinux settings, for example.
(For further questions, it might be best to create a new troubleshooting thread, though this particular error generally indicates something outside of XF's control.)