@ChloeB33 As per my analysis, when you search within SharePoint list, search results will be shown in "List" view and not in "Gallery" view. So, this is not specific to JSON formatting as search results are shown in list view by default.
Also, there is no way to change it to "Gallery" view from search results page:
Please click Mark as Best Response & Like if my post helped you to solve your issue. This will help others to find the correct solution easily. It also closes the item. If the post was useful in other ways, please consider giving it Like.