Programmatically appending to NavigationStack path behaves differently than using NavigationLink

Question

I have a basic log-in flow on a project I'm working on and wanted to try out the new programmatic navigation in SwiftUI from iOS 16. I noticed that appending to the path array after pressing a Button for example made transitions behave differently than using a NavigationLink. This gif illustrates the differences clearer. My theory is the view makes space for the toolbar that appears in the next view and gets redrawn right before it goes offscreen. I'd like some help understanding the differences between these two ways of navigating.

Here is what I have set up regarding the NavigationStack and the state of the path array within an ObservedObject.

enum Path {
    case welcome
    case login
}

class AppState: ObservableObject {
    @Published var path: [Path] = []
}

@main
struct MainApp: App {
    @ObservedObject var appState = AppState()
    
    var body: some Scene {
        WindowGroup {
            NavigationStack(path: self.$appState.path) {
                // Root View
                SplashView()
                    .navigationDestination(for: Path.self) { path in
                        switch path {
                        case .welcome:
                            WelcomeView()
                        case .login:
                            LoginView()
                        }
                    }
            }
            .environmentObject(self.appState)
        }
    }
}

These are the NavigationLink/Button being called from my WelcomeView:

NavigationLink(value: Path.login) {
    RoundedRectangle(cornerRadius: 10)
        .foregroundColor(.black)
        .frame(maxWidth: .infinity)
        .frame(height: 55)
        .overlay {
            Text("NavigationLink Login")
                .font(.custom("Poppins-SemiBold", size: 14))
                .foregroundColor(.white)
        }
}

Button {
    self.appState.path.append(.login)
} label: {
    RoundedRectangle(cornerRadius: 10)
        .foregroundColor(.black)
        .frame(maxWidth: .infinity)
        .frame(height: 55)
        .overlay {
            Text("Button Login")
                .font(.custom("Poppins-SemiBold", size: 14))
                .foregroundColor(.white)
        }
}

Thanks!