This edited TransparentButton improves on my previous answer and no longer overrides to OnPaint. It requires no custom drawing. Instead, it uses Graphics.CopyFromScreen to make a screenshot of the rectangle behind the button and sets its own Button.BackgroundImage to the snipped bitmap. This way it's effectively camouflaged and appears transparent while still drawing as a Standard styled button.

Requirements:

• Create a button with transparent background.
• Do it without drawing the background manually in OnPaint.
• Keep the Button.FlatStyle as FlatStyle.Standard.
• Do not disturb the rounded edges of the standard button.

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class TransparentButton : Button
{        
    public TransparentButton() => Paint += (sender, e) =>
    {
        // Detect size/location changes
        if ((Location != _prevLocation) || (Size != _prevSize))
        {
            Refresh();
        }
        _prevLocation = Location;
        _prevSize = Size;
    };
    Point _prevLocation = new Point(int.MaxValue, int.MaxValue);
    Size _prevSize = new Size(int.MaxValue, int.MaxValue);
    public new void Refresh()
    {
        if (!DesignMode)
        {
            bool isInitial = false;
            if ((BackgroundImage == null) || !BackgroundImage.Size.Equals(Size))
            {
                isInitial = true;
                BackgroundImage = new Bitmap(Width, Height);
            }
            if (MouseButtons.Equals(MouseButtons.None))
            {
                // Hide button, take screenshot, show button again
                Visible = false;
                BeginInvoke(async () =>
                {
                    Parent?.Refresh();
                    if (isInitial) await Task.Delay(250);
                    using (var graphics = Graphics.FromImage(BackgroundImage))
                    {
                        graphics.CopyFromScreen(PointToScreen(new Point()), new Point(), Size);
                    }
                    Visible = true;
                });
            }
            else
            {
                using (var graphics = Graphics.FromImage(BackgroundImage))
                graphics.FillRectangle(Brushes.LightGray, graphics.ClipBounds);
            }
        }
        else base.Refresh();
    }
    protected override void OnMouseUp(MouseEventArgs mevent)
    {
        base.OnMouseUp(mevent);
        Refresh();
    }
    /// <summary>
    /// Refresh after a watchdog time delay. For example
    /// in response to parent control mouse moves.
    /// </summary>  
    internal void RestartWDT(TimeSpan? timeSpan = null)
    {
        var captureCount = ++_wdtCount;
        var delay = timeSpan ?? TimeSpan.FromMilliseconds(250);
        Task.Delay(delay).GetAwaiter().OnCompleted(() =>
        {
            if (captureCount.Equals(_wdtCount))
            {
                Debug.WriteLine($"WDT {delay}");
                Refresh();
            }
        });
    }
    int _wdtCount = 0;
}

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Design Mode Example

Main form BackgroundImage to main form with a Stretch layout. Then overlay a TableLayoutPanel whose job it is to keep the button scaled correctly as the form resizes. TransparentButton is now placed in one of the cells.

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Test

Here's the code I used to test the basic transparent button as shown over a background image:

public partial class MainForm : Form
{
    public MainForm() => InitializeComponent();
    protected override void OnLoad(EventArgs e)
    {
        base.OnLoad(e);
        buttonTransparent.ForeColor = Color.White;
        buttonTransparent.Click += onClickTransparent;
    }
    private void onClickTransparent(object? sender, EventArgs e)
    {
        MessageBox.Show("Clicked!");
        buttonTransparent.RestartWDT();
    }
    protected override CreateParams CreateParams
    {
        get
        {
            const int WS_EX_COMPOSITED = 0x02000000;
            // https://stackoverflow.com/a/36352503/5438626
            CreateParams cp = base.CreateParams;
            cp.ExStyle |= WS_EX_COMPOSITED;
            return cp;
        }
    }
}

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Revision 2.0 Demo

The Master commit now demonstrates a draggable, clickable transparent button over a RichTextBox control.