Well if you go by FDA's Title 21 Chapter I Subchapter B Part 131 Subpart B then not only is human milk not a dairy product but the only animal who produces milk is a cow, however in 2018 they requested submissions weighing in on whether plant products should continue to use "dairy group" words such as milk and yogurt on their labeling, so I think there is probably some leeway on this.

And we all know how trustworthy Google Search is...