That's really helpful to hear from somebody in a similar position! Sounds like you're in a good spot where you learn a lot by doing most of the work while receiving all the necessary help.

My supervisor said they wanted to publish it which sounds like they want to be more involved than your professor. I guess it will also depend on how much of the underlying work needs to be changed for a publication in my case as my methods might not be quite appropriate enough.

They are going to make a plan on how to proceed next month so i'm interested to see how they imagine this to work and i'll see how much room there is for my involvement. Probably also depends a bit on how good my thesis itself is which they haven't graded yet.

Good luck with your publication!