I believe ACF runs a function through that array to display it, or uses some kind of code to parse through the array. It means that not the checkbox HTML is stored in the custom field, but some kind of array values, that are transformed into checkboxes.
You can ask the ACF author how the checkbox array is transformed into actual HTML checkboxes, then I might be able to suggest a customization or filter function to append the transformed code to the result list. It's probably going to be some kind of function or a small snippet from the ACF plugin code.Best,
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