SwiftUI - TabView - How to update $selectedPage from a swipe?

I'm struggling with getting SwiftUI to work with swipes as well as a button for a TabView to scroll and track its order.

So, I have a button that the user can touch to advance the page and the text in the button will change when they get to the end.

However, when they change the page using a swipe the button text doesn't change.

struct MyPageView: View
{
  @State private var selectedPage: Int    = 0
  @State private var buttonLabel : String = "Next"
  
  var body: some View
  {
    ZStack
    {
      Color.black
      
      VStack
      {
        TabView(selection: $selectedPage)
        {
          Page1().tag(0)
          Page2().tag(1)
          Page3().tag(2)
          Page4().tag(3)
          Page5().tag(4)
        }
        .tabViewStyle(.page)
        .indexViewStyle(.page(backgroundDisplayMode: .always))
        
        Button(buttonLabel)
        {
          withAnimation
          {
            selectedPage += 1
            
            if self.selectedPage > 4
            {
              selectedPage = 0
              buttonLabel = "Next"
            }
            else if self.selectedPage == 4
            {
              buttonLabel = "Continue"
            }
            else
            {
              buttonLabel = "Next"
            }
          }
        }
        .buttonStyle(.borderedProminent)
      }.padding(.all)
    }
    .edgesIgnoringSafeArea(.all)
  }
}

How can I get that working so they can tap AND/OR swipe?

Instead of having buttonLabel be a @State variable, it can just be a computed variable:

    @State private var selectedPage: Int    = 0
    
    var buttonLabel: String {
        selectedPage == 4 ? "Continue" : "Next"
    }

That way, it provides the correct value no matter where selectedPage was modified from.

Full:

struct MyPageView: View
{
    @State private var selectedPage: Int    = 0
    
    var buttonLabel: String {
        selectedPage == 4 ? "Continue" : "Next"
    }
    
    var body: some View
    {
        ZStack
        {
            Color.black
            
            VStack
            {
                TabView(selection: $selectedPage)
                {
                    Text("Page 1").tag(0)
                    Text("Page 2").tag(1)
                    Text("Page 3").tag(2)
                    Text("Page 4").tag(3)
                    Text("Page 5").tag(4)
                }
                .tabViewStyle(.page)
                .indexViewStyle(.page(backgroundDisplayMode: .always))
                
                Button(buttonLabel)
                {
                    withAnimation
                    {
                        selectedPage += 1
                        
                        if self.selectedPage > 4
                        {
                            selectedPage = 0
                        }
                    }
                }
                .buttonStyle(.borderedProminent)
            }.padding(.all)
        }
        .edgesIgnoringSafeArea(.all)
    }
}