To add a product carousel in Squarespace, you can use Summary Block or List Section (People Section), then you can pull products from Shop Page.
A. Summary Block
#1. First, ADD BLOCK
#2. Choose Summary
#3. Edit Summary and click Select a Page
#4. Choose your Shop/Product Page
#5. In Design, choose Carousel
#6. With Summary Block Carousel, you cannot adjust the number of items/rows on Mobile. Quite complicated to intervene with the code.
B. List Section (People Section)
#1. First, you need to find Shop/Product Page URL, by clicking Gear icon
and this is URL. In my example, it is: /shop
#2. First, ADD SECTION
#3. Click People (left side) then choose a layout with (i) icon (right side)
#4. Hover on People Section > Click EDIT CONTENT
At Elements > Enable Title
At Content, click Title
and enter Shop Page URL (URL in step #1)
{sync=enter page url}
for example {sync="/shop"}
#5. At Design, choose Carousel
#6. Install this plugin. Plugin will connect People Section with Products in Shop Page.
Plugin will give you some code, to add to Code Injection Header/Footer
#7. Done. Save and Reload the site. Result.