The only real solution is to use a child theme on the site where the local JSON is defined in the parent theme and there is no local JSON folder in the child theme. Then you can set a second load path to load the JSON files in the parent theme https://www.advancedcustomfields.com/resources/local-json/
A solution for saving local JSON for and fields created in the child theme sub site would be to create a place outside of the theme to save and load field groups in the child theme. For example, when the theme is activated you can create an acf-json folder in wp-content/uploads/sites/{$site_id}/ and set the save and load points for the child theme to this location and this would create a unique location for json files for each site.
