Export/transfer TT3 changes while still being able to update

I think this might be a basic question, but I (a self-taught amateur) have not been able to figure it out and can’t find a relevant forum post or documentation.

I customized the TT3 theme on a test WP install before using the export feature in the site editor and importing it into my live site. This created a new theme called TwentyTwentyThree2, which is what I’m currently running. However, this process seems to have broken the connection to update the theme when a new version of TwentyTwentyThree is released. I tried copying my theme folder and renaming it TwentyTwentyThree, but that did not fully work (only some changes were copied over, but not things like the navigation bars or many of my design changes). All of my changes have been done using the site editor. Where are these changes stored, and how can I move copy them into the official TT3 theme on my site? Thank you for your help.

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