theme.json should be in the child theme folder when using xxxx.json style located in the styles folder?

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

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