If you’re going to have a parent/child theme layout, if this was me I’d actually put the JSON in the parent theme and either add a load location or load them manually. But that would be your call. I personally think the less code that’s needed in a child theme the better.
If there is already and existing page to use as an example you could use ACF to get the values from a “Template” post and insert them into the new post when it’s created. Or you could output all of the values from a “Template” post and hard code them into an array and then use that array to generate a new post. To be honest there’s a lot of ways that something like this could be done, but I don’t think there is any automatic way to copy everything from one post to another when a new post is created… well, there is, but nothing that I know of that can be called from code when someone clicks on “Add New” https://wordpress.org/plugins/duplicate-post/
