Note that Geany is a portable GTK application available on Gnome, KDE, Xfce, Windows, Macos so it does not use any desktop specific APIs
To be clear, Gedit is a [Gnome](https://wiki.gnome.org/Apps/Gedit) application, it is "integrated with that desktop" to quote the linked page, not a plain GTK application like Geany.
As @ineuw says Libreoffice has the resources to maintain integration with individual desktops, so for example Debian has a [libreoffice-gnome](https://packages.debian.org/sid/libreoffice-gnome) integration package and I am aware of an evolution integration package and I am sure it has specific integration with Windows and Macos.