No need to break these up. I never do. You can leave the gtk-3.0 and gtk-4.0 folders inside the parent theme folder.Many current themes package GTK 3 and GTK 4 parts together, so you have to break them up manually to put them into the correct folders. GTK 4 themes should handle your main menus and the most up to date apps.
gtk-3/4 themes you download will not theme Gnome Core Applications (such as Files, Disks, etc) that are using libadwaita to control their appearance. If you want a uniform appearance for all your applications, you must use one of the Adwaita themes for the Legacy applications theme choice.
gnome-shell theme versions should match the gnome-shell version in order to appear as intended. Check before downloading.
"Extensions" is not the best tool to manage gnome-shell extensions, since it will not install them. Use "Gnome Shell Extension Manager" instead.
You can control accent colors when not using a Yaru theme with "Custom Accent Colors" gnome-shell extension.
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