By default Ubuntu Core is a headless system that only allows setting up a single user and is operated via ssh.
There are currently no proper desktop environments (though there is some experimental work from @jamesh), when using graphical output Ubuntu Core is typically used for “single app kiosks” or digital signage systems.
To run VNC you would obviously need a running desktop on the Ubuntu Core device …
Also an experiment, but installable from the snap store is:
But that has no support for VNC
Has this changed in 2022? Ubuntu Core looks great, but a desktop is a requirement for us - this lack of functionality prevents us from moving to Ubuntu Core. Using XRDP with VNC allows remote users running Windows to RDP into our device for remote administration/troubleshooting. It is also useful for our remote and QA personnel to troubleshoot right at the device.