Set up your SquareUp Marketplace.
Create your widget in SquareUp for your shop. (SquareUp - Business Settings - Promote - Menu Embed.)
Copy your new code.
Go to your Squarespace site and use the </> embed code block. Put your SquareUp widget in this code block.
When you click "edit" on the code, you can change any of the hex colors to match your brand on your site.
A lovely shop now exists within your website in the widget. Only upon final checkout is the client redirected into your marketplace on Square.
If you need to make changes to what is shown online - those changes are made in your SquareUp account. The only items that will show on your site are items that are marked as "make this item available for sale online". Any changes automatically update in the widget.
It's pretty rad.