On Ubuntu (and probably other distros that use Systemd as well) you need to enable the user service manually once for your user:
systemctl --user enable --now syncthing.service
This will start syncthing whenever your user session is active. By default that means when you login. If you run this command: sudo loginctl enable-linger $USER
Then your user service manager will be started at boot and run regardless if you are logged in or not. (The default behavior makes more sense on desktop and laptop computers.)