The data you’re talking about being saved in a serialized array is data saved by WP. ACf stores data for widgets consistent with the way is saves data for all fields it manages.
I was curious so I looked into it a bit more. Rather than just say I don’t thinks is possible I thought I would explain why.
Saving this information along with the standard widget information would require hooking into where WP saves the data for a widget. Unfortunately WP does not provide any hooks in the core widgets that will let you do this, and since WP doesm’t do it I doubt that widget authors do it either. Without these hooks it’s not possible to make this happen.
If there was a way to hook into the widget save then you’d also need to hook into the load_value hook of ACF to get the current values from the widget. This part would be completely possible if you could do the first part.
To export and import you’d need a plugin that’s aware of ACF. I don’t think there is one.
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