How to number figures inside footnotes I cannot think of an instance where I saw a figure inside a footnote in any published work, but in my specific case it seems appropriate to put one there.
However, since this is a rather uncommon thing to do, I am not sure how to label the figure's caption.
As @Alan Munn also pointed out in a comment to this answer, it seems odd to include it in the normal figure numbering, since - at least in the field of linguistics - numbering for examples etc. is separated from the main text.
As shown in the screenshot below, the figures in the main text are counted within chapters (Figure chapter.figure:), and examples in footnotes are numbered with the common lowercase roman numerals.
I will only add one or two lines to this note and its contents are a typical case for footnote examples, which is why I do not want to include it in the main text. Really the only odd thing is the additional figure showing the pitch of said example.

Are there any typographic/academic/editorial standards for this?
I am not sure how to label [a figure that appears in a footnote]

Presumably the figure is relevant only to the footnote, otherwise it wouldn't appear in the footnote: Include the figure without numbering and without a caption, explain the figure in the footnote.