I had a theoretical look at this:
* [Mint-Y-Sand theme](https://github.com/linuxmint/mint-themes/blob/master/files/usr/share/themes/...) uses the [Mint-Y-Sand icon theme](https://github.com/linuxmint/mint-y-icons/blob/master/usr/share/icons/Mint-Y...) * [Mint-Y-Sand icon theme](https://github.com/linuxmint/mint-y-icons/blob/master/usr/share/icons/Mint-Y...) inherits from (in order): [Mint-Y](https://github.com/linuxmint/mint-y-icons/blob/master/usr/share/icons/Mint-Y...), Adwaita, gnome, hicolor. It provides [very few icons itself](https://github.com/linuxmint/mint-y-icons/tree/master/usr/share/icons/Mint-Y...) * [Mint-Y](https://github.com/linuxmint/mint-y-icons/blob/master/usr/share/icons/Mint-Y...) provides [more icons](https://github.com/linuxmint/mint-y-icons/tree/master/usr/share/icons/Mint-Y), but doesn't seem to provide everything we use, including e.g. neither `gtk-new` nor `document-new`.
Thus, it falls back to Adwaita for those. So everything seems normal, except that Geany shows more icons than this theme was really meant to.