There isn’t any way to have a field group on just images. I’ve tried several times to create such a rule but this information is not available in the standard wp media gallery, that’s the one with the thumbnails that loads in a modal window. If I remember correctly it is possible to create custom location rules by file type if you use the list view in the media library instead of the grid view, this is because the post editor is used for editing them this way.
As far as buttons in the gallery, the gallery field does not support additional fields, any additional fields are attached to the individual images and not to the gallery.
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