you can try to get XWMHints, it has a member named icon_pixmap. and you can try to find icon file too, detail:

specifications.freedesktop.org/icon-theme-spec/icon-theme-spec-latest.html

My WM have 3 ways to get icon, detail:

https://sourceforge.net/p/gsmwm/code/ci/master/tree/src/image.c