There is a topic here that appears to have a solution for auto syncing https://support.advancedcustomfields.com/forums/topic/automatic-synchronized-json/.
That being said, I’m not sure I’d worry about it. I currently have a multisite install where I have the same situation. The same theme and ACF fields are used on all sites. Not only this, but I have to “dev” copies of this multisite install. When I make changes on one site I then sync all of the files, like you. But then I don’t bother syncing the ACF fields, this is not necessary as the JSON files will be used and override what is in the database. The next time I work on a site, if I need to make changes to the fields, I sync the field groups for the site I and group I am currently working on. If the client was going to take over this, I would assume that they are capable to doing this as well.
