@State with a @Appstorage property does not update a SwiftUI View

Question

I organized some settings to be stored in UserDefauls in a struct like this, because I want to have them in one place and to have getters and Setters.

enum PrefKeys : String {
  case KEY1
  case KEY2
  
  var key: String  { return self.rawValue.lowercased()}
}

struct Preferences {
  @AppStorage(PrefKeys.KEY1.key) private var _pref_string_1 = ""
  @AppStorage(PrefKeys.KEY1.key) var pref_string_2 = ""
  
  var pref_string_1: String {
    set { _pref_string_1 = newValue.lowercased() }
    get { return _pref_string_1.lowercased() }
  }
}

using it like this works fine:

struct ContentView: View {
  var p = Preferences()
  
  var body: some View {
    NavigationView{
      VStack(alignment: .leading){
        Text("pref_string_1: \(p.pref_string_1)")
        Text("pref_string_2: \(p.pref_string_2)")
        NavigationLink("Sub",destination: SubView())
      }
    }
    .padding()
  }
}

If I use p as a @State var, it does not update the view, when the @State var is changed:

struct SubView: View {
  @State  var psub = Preferences()
  @AppStorage("standalone pref") private var standalonePref = ""
  
  var body: some View {
    VStack(alignment: .leading){
      Text("Preference1 in struct: \(psub.pref_string_1)")
      TextField("Preference1 in struct:", text: $psub.pref_string_1)
      
      Text("standalonePref \(standalonePref)")
      TextField("standalonePref:", text: $standalonePref)
    }
  }
}

How can I fix this?