Wayland doesn’t have a concept of window icons, so gtk_window_set_icon_*() are not implemented in the gdk wayland backend.
The icon in the window switcher comes from the .desktop file, which means that gnome-shell must be able to match the window to the application. This requires setting the application id to match the .desktop file. The best way to do this is with GtkApplication and either GtkApplicationWindow or gtk_window_set_application(), but you can fix this minimally with:
g_set_prgname("org.pwmt.zathura");
For historical reasons, this call is recommended for GTK 3 even if you do use GtkApplication. Otherwise, the xdg-shell app_id will not match.