GTK will use SSD so long as you don’t customise the title bar. I think you can even query it, with effort (gdk_wayland_display_prefers_ssd, c.f. https://gitlab.gnome.org/GNOME/gtk/-/commit/f2adaba237519642...), and thus behave differently depending on compositor preference. (But even that is mildly nerfed from the org_kde_kwin_server_decoration_manager interface, since it only exposes “prefers SSD” and not “supports SSD”—though in practice I suspect there’s no difference in any compositor.)
But guess what? GTK 4 has regressed matters in this space. Fancy that. If I run gtk3-demo, as a tiled window it gets Sway SSD and an app header bar which duplicates the title (fine), but it doesn’t have the window border or shadow (good). When I float the window, it gets border (including top radii) and shadow. This is well-behaved software, not acting quite how I’d prefer it to (I want SSD even floating, even double-title-barring), but still reasonably. But gtk4-demo? It gets border and shadow (drawing outside its designated area even in tiling mode, and I’m not sure why it’s possible for it to do that) regardless of whether it’s floating or not. Progress. They’re forging ahead with ignoring the existence of SSD as far as possible even in GTK.