If you put your field groups into PHP and the file is loaded by all sites then they will work on all sites.
JSON files should work on all sites if they are loaded by all sites and syncing should not be needed. I have a couple of site in multisite that use JSON files. Not only do I not sync the groups to all sites, but they don’t even exist in the DB for sub sites, only the main site. All of the sites use the same theme so any changes I make to the field groups are automatically reflected in the sub sites. The only place the DB version of any site is used is when you edit the field group. Under all other conditions, if the field group exists as json then the json will be loaded.
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