@Dan Schmitz I have done this for multiple companies not on squarespace but other platforms. Whenever you rebuild your website expect some effects on your SEO, but again it depends on what the current traffic is and what are you ranking for and if changes that you make interms of content on your website are in line with what you rank for.
But if you are just recreating the entire website as-is, effects would be minimal.
In my experience atleast