Quiz content and settings (questions, products, design) are stored in PerfectMatch: AI Shopping Quiz and are not affected by theme changes. However, the quiz block placement in the Theme Editor is theme-specific — you'll need to re-add the PerfectMatch: AI Shopping Quiz block to your new theme after switching.
After activating your new theme, go to Online Store → Themes → Customize.
Add the PerfectMatch: AI Shopping Quiz block to the desired pages and sections.
Select which quiz to display and save.