userInterfaceStyleChangedObserveMethod.swift

extension Reactive where Base == UIScreen {
    @available(iOS 13.0, *)
    func userInterfaceStyle() -> Observable<UIUserInterfaceStyle> {
        let currentUserInterfaceStyle = UITraitCollection.current.userInterfaceStyle
        let initial = Observable.just(currentUserInterfaceStyle)
        let selector = #selector(UIScreen.traitCollectionDidChange(_:))
        let following = self.base
            .rx
            .methodInvoked(selector)
            .flatMap { (args) -> Observable<UIUserInterfaceStyle> in
                return Observable.just(UITraitCollection.current.userInterfaceStyle)
        }
        return Observable.concat(initial, following)
    }
}

    @available(iOS 13.0, *)
    private func observeUserInterfaceStyle() {
        UIScreen.main.rx
            .userInterfaceStyle()
            .subscribe(onNext: { [weak self] userInterfaceStyle in
                print("userInterfaceStyle changed to: \(userInterfaceStyle.description)")
                self?.loadAppStyleSheet()
            })
            .disposed(by: disposeBag)
    }

Thank you! Very helpful when trying to observe the system setting while the window's overrideUserInterfaceStyle is set.

One idea is I think you could combine lines 10 and 11 to just map { _ in UITraitCollection.current.userInterfaceStyle }
Also you could use startWith(currentUserInterfaceStyle) instead of making a second observable and concatenating

If you don't want it to fire when irrelevant traits change, you could also add a filter on previous?.userInterfaceStyle != UITraitCollection.current.userInterfaceStyle (or map to userInterfaceStyle and then call distinctUntilChanged)