I had the exact same problem and the answer was not obvious. I’m pretty new to WP, so very possibly it is explained somewhere and I just didn’t look hard enough.
I believe it’s a matter of converting JSON files from one theme and moving them to the other for Styles, and I would guess similar for templates/template parts.
Anyway, I just ended up manually rebuilding my templates, template parts and my custom style.json in TT3. Hopefully there is a better way. Good luck!