Resolve Data Refresh Conflict

I think you're on the right track with adding a boolean value in the Model. What could make this successful is to give the textbox a concept of direction. One approach you could experiment with is to allow incoming value refresh only when the textbox is ReadOnly. Then (for example) by double-clicking on the textbox, the direction can be effectively changed to 'outgoing' until the SendChangeMessage commit is completed. An additional binding for textbox.ReadOnly has been added to the Model.

    public MainForm()
    {
        InitializeComponent();
        // Set bindings
        textbox.DoubleClick += (sender, e) =>
        {
            textbox.BeginInvoke(() =>
            {
                textbox.ReadOnly = false;
                textbox.SelectAll();
            });
        };
        textbox.KeyDown += (sender, e) =>
        {
            switch (e.KeyData) 
            {
                case Keys.Enter:
                    if (!textbox.ReadOnly)
                    {
                        e.Handled = e.SuppressKeyPress = true; 
                        SendChangemessage(textbox.Text);
                        textbox.ReadOnly = true;
                    }
                    break;
            }
        };
        textbox.LostFocus += (sender, e) =>
        {
            if(this == ActiveForm) textbox.ReadOnly = true;
        };
        textbox.DataBindings.Add(
            new Binding(
                propertyName: nameof(TextBox.Text),
                dataSource: Model,
                dataMember: nameof(Model.Value),
                formattingEnabled: false,
                dataSourceUpdateMode: DataSourceUpdateMode.OnPropertyChanged
        ));
        textbox.DataBindings.Add(
            new Binding(
                propertyName: nameof(TextBox.ReadOnly),
                dataSource: Model,
                dataMember: nameof(Model.IsReadOnly),
                formattingEnabled: false,
                dataSourceUpdateMode: DataSourceUpdateMode.OnPropertyChanged
        ));
    }
    MainFormViewModel Model { get; } = new MainFormViewModel();

Outgoing change message

    private void SendChangemessage(string text) =>
        MessageBox.Show(text, "Change Message");

Mock Update from Server with random values

    protected override void OnLoad(EventArgs e)
    {
        base.OnLoad(e);
        _ = ExecRefreshLoop();
    }

    private async Task ExecRefreshLoop()
    {
        while(!Disposing)
        {
            if (Model.IsReadOnly) 
            {
                Model.Value = Random.Next(1000, 10000);
            }
            await Task.Delay(TimeSpan.FromSeconds(1)); 
        }
    }
    private Random Random { get; } = new Random();
}

---

Mock Binding Values class

Typical view model that can act as a binding context for the entire MainForm

public class MainFormViewModel : INotifyPropertyChanged
{
    public int _value;
    public int Value
    {
        set
        {
            if (value != _value)
            {
                _value = value;
                OnPropertyChanged();
            }
        }
        get { return _value; }
    }
    public bool IsReadOnly
    {
        get => _IsReadOnly;
        set
        {
            if (!Equals(_IsReadOnly, value))
            {
                _IsReadOnly = value;
                OnPropertyChanged();
            }
        }
    }
    bool _IsReadOnly = true;

    public event PropertyChangedEventHandler? PropertyChanged;
    protected virtual void OnPropertyChanged([CallerMemberName] string? propertyName = null)
    {
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
    }
}