Whatever you do it will require updating every site. There are many ways to do that updating. It really depends on how complex you want to get.
Almost anything you do will involve using local JSON.
This is what I do.
I create custom themes. Any site I build uses a child theme on one of my custom themes. The parent theme uses local JSON files in acf-json folder. I keep the parent theme in a private repo on GitGHub and it can be updated from there. That is a quick description, there is a lot involved in getting this set up.
You could also do this by creating a plugin that has just the JSON files in it and load the field groups from your plugin. This would allow you to keep the field groups updated without affecting the theme. I have several plugins that use ACF fields in this way. Usually not field groups for themes though, these are usually specific to the plugin.
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