Many icons are used as an overlay, where the content is in one of the corners. To show where inside the area the content is placed, we could choose to use a border and/or a background for the icon in the SidePanel. It would help users see and find the right icon for the right situation.

Example of a border, a background and both:

Further, it would show that a few icons seem to have a variable aspect ratio - they're not square. I saw a couple related to Punctuation.