Hi, @abalogh! Welcome to the Vercel Community 
Happy to help out here 
It’s so great to hear that you’ve built a great app on v0! We’d love to share it in the community once you’ve fully shipped.
Appreciate the feedback! As of today, we don’t have a git repo connection that allows that “local” editing experience. Right now, if you want to continue using v0, you will have to continue using it from the current chat and keep deploying new changes from there. You can think of it almost as your IDE (note: at it’s current state)
Alternatively, if you want to keep editing in your local machine and “take control” with no more interactions with v0, you can Add to Codebase and run the command in your console. Then you can push that project up to your git provider.
I’ve done this for a few projects, but do note that I am familiar as I was a software engineer back in the day 
From your post it sounds like you’d like to keep iterating on v0, is that right?
Hopefully that helps! Let me know if you have any more follow-up questions.
We also have run some v0 community content, might be helpful for you: