The Share dialog shows the property’s cover photo beside its name automatically. This requires HomeRunner Toolkit 3.277.0 or later, so update the Toolkit if you do not see the photo yet.
The photo comes from the property’s featured image. When no featured image is set, the dialog uses the first listing photo instead. There is nothing to configure. On a page with no photo, the dialog looks as it did before.
On phones, the device’s own share sheet still opens first, as documented in the Property Actions article.