I'm making a child theme of TT3. I'm using a json style in my child theme located in a styles named folder. Do I have to have a copy of TT3 theme.json in my child theme ?
Short answer: No
Long answer: The child themes theme.json will simply use the TT3 theme.json values if a specific value is not found. So you can make a new theme.json file only with the specific values needed for the child theme.
An excellent writeup is available here: https://kinsta.com/blog/twenty-twenty-two-theme/#extending-twenty-twentytwo-with-a-child-theme