Review widget schema markup?

Does anyone know if the review widget has the JSON schema markup for reviews/products so that google will pickup the star rating for the homes and our websites in general?

Currently the review widget doesn't have the JSON schema markup as we're not sure it would work in an iframe or when added via javascript.

We're open to adding the JSON-LD for reviews on the widget if we can confirm it would show on the correct page when embedded that way, but are wary of adding without confirmation as Google's crawling can be a bit finicky for the reviews.

add schema markup to the page (or overall site)  itself, not to the widget.