ColorScheme.swift

//
//  ColorSchemeApp.swift
//  ColorScheme
//
//  Created by Craig Hockenberry on 9/11/24.
//

import SwiftUI

@main
struct ColorSchemeApp: App {
	@AppStorage("preferredColorScheme") private var preferredColorScheme: ColorScheme?

    var body: some Scene {
        WindowGroup {
            ContentView()
				.preferredColorScheme(preferredColorScheme)
        }
		.onChange(of: preferredColorScheme) { oldValue, newValue in
			print("ColorSchemeApp: preferredColorScheme: \(oldValue) -> \(newValue)")
		}
    }
}

// NOTE: This allows @AppStorage to store an optional ColorScheme
extension ColorScheme: RawRepresentable {
	
	public init?(rawValue: Int) {
		guard let userInterfaceStyle = UIUserInterfaceStyle(rawValue: rawValue),
			  userInterfaceStyle != .unspecified,
			  let colorScheme = ColorScheme(userInterfaceStyle)
		else {
			//print("ColorScheme init: colorScheme = nil, rawValue = \(rawValue)")
			return nil
		}
		//print("ColorScheme init: colorScheme = \(colorScheme), userInterfaceStyle = \(userInterfaceStyle)")

		self = colorScheme
	}
	
	public var rawValue: Int {
		let userInterfaceStyle = UIUserInterfaceStyle(self)
		//print("ColorScheme rawValue: self = \(self), userInterfaceStyle = \(userInterfaceStyle)")
		return userInterfaceStyle.rawValue
	}

}

// NOTE: This provides a display name for an optional ColorScheme
extension ColorScheme? {

	public var displayName: String {
		if let self {
			switch self {
			case .dark: return "Dark"
			case .light: return "Light"
			@unknown default:
				return "Unknown"
			}
		}
		else {
			return "System"
		}
	}
}

struct ContentView: View {
	
	@State private var presentSettings = false
	
	@State private var identityHack: Int = 0

	@AppStorage("preferredColorScheme") private var preferredColorScheme: ColorScheme?

	var body: some View {
		VStack(spacing: 40) {
			Text(preferredColorScheme.displayName).font(.headline)
						
			Button("Show Settings") {
				presentSettings = true
			}
		}
		.padding()
		.sheet(isPresented: $presentSettings) {
			SettingsView()
				.id(identityHack) // an attempt to force an update by changing structural identity
				.preferredColorScheme(preferredColorScheme)
				.onChange(of: identityHack) { oldValue, newValue in
					print("SettingView: identityHack: \(oldValue) -> \(newValue)")
				}
		}
		.onChange(of: preferredColorScheme) { oldValue, newValue in
			print("ContentView: preferredColorScheme: \(oldValue) -> \(newValue)")
			identityHack += 1
		}
	}
}

struct SettingsView: View {
	
	@Environment(\.dismiss) private var dismiss
	
	@State private var path = NavigationPath()
		
	@AppStorage("preferredColorScheme") private var preferredColorScheme: ColorScheme?
	
	var body: some View {
		NavigationStack(path: $path) {
			Form {
				Section {
					Picker("Theme", selection: $preferredColorScheme) {
						Text("System").tag(nil as ColorScheme?)
						Text("Dark").tag(ColorScheme.dark as ColorScheme?)
						Text("Light").tag(ColorScheme.light as ColorScheme?)
					}
				}
			}
			.toolbar {
				ToolbarItem(placement: .confirmationAction) {
					Button("Done") {
						dismiss()
					}
				}
			}
		}
	}
}

#Preview {
	ContentView()
}

A full working solution is below:

//
//  ColorSchemeApp.swift
//  ColorScheme
//
//  Created by Craig Hockenberry on 9/11/24.
//

import SwiftUI

@main
struct ColorSchemeApp: App {
	@AppStorage("preferredColorScheme") private var preferredColorScheme: ColorScheme?

    var body: some Scene {
        WindowGroup {
            ContentView()
				.preferredColorScheme(preferredColorScheme)
        }
    }
}

// NOTE: This allows @AppStorage to store an optional ColorScheme
extension ColorScheme: RawRepresentable {
	
	public init?(rawValue: Int) {
		guard let userInterfaceStyle = UIUserInterfaceStyle(rawValue: rawValue),
			  userInterfaceStyle != .unspecified,
			  let colorScheme = ColorScheme(userInterfaceStyle)
		else {
			return nil
		}

		self = colorScheme
	}
	
	public var rawValue: Int {
		let userInterfaceStyle = UIUserInterfaceStyle(self)
		return userInterfaceStyle.rawValue
	}

}

// NOTE: This provides a display name for an optional ColorScheme
extension ColorScheme? {

	public var displayName: String {
		if let self {
			switch self {
			case .dark: return "Dark"
			case .light: return "Light"
			@unknown default:
				return "Unknown"
			}
		}
		else {
			return "System"
		}
	}
	
}

struct ContentView: View {
	
	@State private var presentSettings = false
	
	@AppStorage("preferredColorScheme") private var preferredColorScheme: ColorScheme?

	@Environment(\.colorScheme) private var colorScheme

	var body: some View {
		VStack(spacing: 40) {
			Text(preferredColorScheme.displayName).font(.headline)
						
			Button("Show Settings") {
				presentSettings = true
			}
		}
		.padding()
		.sheet(isPresented: $presentSettings) {
			// NOTE: Using a nil value for .preferredColorScheme() _will not_ update the view. The workaround
			// is to get the current colorScheme from the environment and use it instead (via optional chaining).
			SettingsView()
				.preferredColorScheme(preferredColorScheme ?? colorScheme)
		}
	}
}

struct SettingsView: View {
	
	@Environment(\.dismiss) private var dismiss
	
	@State private var path = NavigationPath()
		
	@AppStorage("preferredColorScheme") private var preferredColorScheme: ColorScheme?
	
	var body: some View {
		NavigationStack(path: $path) {
			Form {
				Section {
					Picker("Theme", selection: $preferredColorScheme) {
						Text("System").tag(nil as ColorScheme?)
						Text("Dark").tag(ColorScheme.dark as ColorScheme?)
						Text("Light").tag(ColorScheme.light as ColorScheme?)
					}
				}
			}
			.toolbar {
				ToolbarItem(placement: .confirmationAction) {
					Button("Done") {
						dismiss()
					}
				}
			}
		}
	}
}

#Preview {
	ContentView()
}

For reference, this method is not fully working and I can't really tell why.

I recorded a short video to showcase the issue (iOS 18 simulator, but same behavior in my device). As you'll see, I can toggle the system color scheme in the beginning and the app changes. However, when I change the setting to 'Dark' and then back to 'System', the app stays dark and no longer updates when the system color scheme changes.

ColorSchemeNotWorking.mp4