Change from WordPress to StudioPress

This theme is ancient:

https://www.ads-software.com/themes/studiopress/

I think you mean:

https://www.studiopress.com/

in which case, you should ask on their support – as these forums don’t support commercial themes.

But in general, no, you don’t need to start over – you’ll just need to set up new theme options and settings in the new theme.