The Advanced Options section you are talking about the one in the Image Details, the modal that shows when clicking here:
that part is tinyMCE, its part of the tinyMCE editor, none of these fields are being saved in the WordPress database:
this is just and interface to gather data that will be set in the <img> tag, it uses JavaScript, the interface is populated when you click in the image if there is any attribute and/or data that was previously set there.
so you cant use WordPress functions to get those classnames.
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