What about the status of the official TOR VPN?

Fartimoji What I understand from the link you provided, the feature to run a virtual machine on the phone is already available for me on my pixel7a, if my phone is on the newest version,
(which is the 2025031400 right now),
but this feature is currently just a "primitive proof of concept" and limited to just a terminal.

That matches my understanding.

Fartimoji What do they mean here with "primitive"?
Just the fact that a different operating system can run " but just limited to a terminal mode"?
Or are there other limitations beside the missing graphical user interface?

I'm sure there are limitations. For example, I would be mildly surprised if non-virtio storage and network were supported (though I haven't looked into it at all, so I could be wrong!).

Or is it possible to run a full functional version of Linux in a virtual machine right now, without limitations of it's functionality?

As indicated above, this feature has not yet shipped for general use. It has lots of limitations. The code is changing fast enough that I suspect it doesn't make sense for anybody to write down exactly what does and doesn't work, because by the time writing finished the software would have changed again. By no means is this feature fully functional!

This feature is experimental, meaning that people who wish to experiment with it can do so. But at this point it doesn't make sense for people to be asking questions about exactly what will and won't be supported (nobody knows!). At this point, nobody knows what will/won't work a month from now, or six months from now. There isn't a roadmap.

Please note that this is just my personal opinion. From time to time the GrapheneOS project makes announcements, in this forum and also on social media.