SwiftUI TextField Display Not Updating When Using Integer Value

I'm trying to make a view similar to the Edit View in one of the Apple SwiftUI tutorials. Specifically, I want to make something similar to how they add attendees, but would like to do it with integers instead of strings. I can mostly get it to work, but for some reason the default value doesn't want to reset when clicking the + button to submit. Example code is below:

import SwiftUI

struct Item: Identifiable {
    public let id = UUID()
    var val: Int
}

struct BrokenView: View {
    @State private var new_value = 0
    @State private var l = [Item(val: 1), Item(val: 2), Item(val: 3)]
    
    var body: some View {
        Form {
            Section(header: Text("Items")) {
                ForEach(l) { item in
                    Text("\(item.val)")
                }
                HStack {
                    TextField("Value", value: $new_value, format: .number)

                    Button(action: {
                        withAnimation {
                            l.append(Item(val: new_value))
                            new_value = 0 // the value gets set correctly, but the new TextField keeps the old value
                        }
                    }) {
                        Image(systemName: "plus.circle.fill")
                    }
                    .disabled(new_value == 0)
                }
            }
        }
    }
}

I tried to implement something like this answer here, but I'm still having the same issue. What am I doing wrong here?

From the TextField docs:
If the value is a string, the text field updates this value continuously.... For non-string types, it updates the value when the user commits their edits, such as by pressing the Return key.

So you could use the following workaround approach, using a String, to get the desired functionality.

struct BrokenView: View {
    @State private var txt = ""  // <-- here, adjust if need be, eg "0"
    @State private var new_value = 0
    @State private var l = [Item(val: 1), Item(val: 2), Item(val: 3)]
    
    var body: some View {
        Form {
            Section(header: Text("Items")) {
                ForEach(l) { item in
                    Text("\(item.val)")
                }
                HStack {
                    // -- here
                    TextField("Value", text: Binding(
                        get: { txt },
                        set: {
                            if let i = Int($0) {
                                new_value = i
                                txt = $0
                            }
                        })
                    )
                    Button(action: {
                        withAnimation {
                            l.append(Item(val: new_value))
                            new_value = 0
                            txt = ""  // <-- here, adjust, eg "0"
                        }
                    }) {
                        Image(systemName: "plus.circle.fill")
                    }
                    .disabled(new_value == 0)
                }
            }
        }

    }
}