Maybe I misunderstand your question, but in order for X11 forwarding to work an X-server needs to be running on the remote machine. The multi-user.target relates to setting up a system in non graphical (console) multi-user mode, while graphical.target is for setting up graphical multi-user system with network services.
multi-user.targetA special target unit for setting up a multi-user system (non-graphical). This is pulled in by graphical.target.
Units that are needed for a multi-user system shall add Wants= dependencies for their unit to this unit during installation. This is best configured via WantedBy=multi-user.target in the unit’s [Install] section.
graphical.targetA special target unit for setting up a graphical login screen. This pulls in multi-user.target.
Units that are needed for graphical logins shall add Wants= dependencies for their unit to this unit (or multi-user.target) during installation. This is best configured via WantedBy=graphical.target in the unit’s [Install] section.