wpgraft reads the page as your browser rendered it, every element and the computed styles on each one, at every breakpoint you ask for, and rebuilds it as Breakdance’s own native elements with the styles in Breakdance’s own fields. It needs no access to your Squarespace account, no export file and no API key. If Chrome can draw the page, wpgraft can copy it.
Squarespace does not let you take your design out, and that is not an oversight. A hosted platform’s layout is its own format and stays that way. So this is not an export. You open the published page, point at the part you want, and it is rebuilt in Breakdance from what was on screen. Your Squarespace site keeps running the whole time, which means you can move one section at a time and switch over when the new one is genuinely better.