How to programatically open Settings/Preferences window in a macOS SwiftUI App

I have created a simple macOS-only SwiftUI app and added a Settings screen as per Apple's instructions:

import SwiftUI

@main
struct MyApp: App {
    var body: some Scene {
        WindowGroup {
            RootView()
        }
        Settings {
            SettingsView()
        }
    }
}

It works: the Preferences option shows up in the app menu. Now, I would also like to open this settings window programatically, e.g. when a button is clicked. Is there a way to achieve this?

I was hoping there would be a method in NSApplication, similar to the About window, but there doesn't seem to be one.

By inspecting the app menu, I found this solution:

NSApp.sendAction(Selector(("showPreferencesWindow:")), to: nil, from: nil)

I assume that it may not pass App Review for using a private API, though, so less shady alternatives are still welcome.

Update: This has actually passed App Review, so I had marked it as the answer.

Update 2: For a macOS 13 solution, see Manny's answer.

Update 3: For macOS 14 with SwiftUI, you must use the new SettingsLink view documented here or OpenSettingsAction as documented here. NSApp.sendAction no longer works.