The feature appears to use browsing history and is compatible with most shopping sites. It is not exclusive to only Google shopping merchants. Through personal exploring, I've found that most large brand retailers, including Gap Brands, Lowes, and Amazon automatically show up. Also, large eCommerce platforms such as Shopify and Woocommerce are compatible. I found that my Gap shopping cart only showed up when I'm logged into both Gap and Google with the same email address. When I shopped Gap as a guest, then the abandoned shopping cart did not (at least immediately) show on my personalized Google Search page. All of my tested Shopify shops show up immediately without requiring a login. Some WooCommerce shops showed up regardless of whether I am logged in to the retailer's WordPress site with my google account email and some did not. Specifically, a European-based Woocommerce site did not show up, perhaps due to cookies/tracking limitations.