What Linux needs before a session will connect, and the two cases where it will not.
X11 required
Screen capture and input injection go through the X11 server. A desktop running under Wayland cannot be captured, and SullTec Remote will connect but show a black screen.
Log out, and at the login screen choose a session marked Xorg or X11 before signing back in. On GNOME the chooser is the gear icon beside the Sign In button. To make it permanent, set WaylandEnable=false in /etc/gdm3/custom.conf and reboot.
Reaching the login screen
Connecting to a machine where nobody has signed in yet needs the client running as a system service rather than as a user. Without it the machine is reachable only once somebody logs in locally, which defeats unattended access.
Confirm the service is enabled with systemctl status sulltecremote. The display manager must also be on X11 — see X11 required above, which applies to the login screen as much as to a desktop session.
Permission problems
If a session connects but input does nothing, the client has screen access without input access. This usually means it is running as a different user than the one holding the desktop session, or that the desktop is Wayland and only the fallback capture is working.
Check that the service user can reach the X display, and that xhost is not restricting it. If the machine has both an X11 and a Wayland session installed, confirm which one is actually in use before changing anything else.