GraphicsDeviceExtensions.cs

using Microsoft.Xna.Framework.Graphics;

public static class GraphicsDeviceExtensions
{
    public static Resolution GetScreenResolution(this GraphicsDevice graphicsDevice)
    {
        var pp = graphicsDevice.PresentationParameters;
        return new Resolution(pp.BackBufferWidth, pp.BackBufferHeight);
    }
}

Resolution.cs

using Microsoft.Xna.Framework;

public readonly struct Resolution
{
    public int Width { get; }
    public int Height { get; }

    public Resolution(int width, int height) =>
        (Width, Height) = (width, height);

    public Matrix ScaleTo(Resolution target, Vector2 offset = default)
    {
        var targetX = Width;
        var targetY = Height;

        var scaleX = target.Width / targetX;
        var scaleY = target.Height / targetY;

        var scale = scaleY * targetX > target.Width
            ? scaleX
            : scaleY;

        var actualX = scale * targetX;
        var actualY = scale * targetY;

        var offsetX = (target.Width - actualX) / 2;
        var offsetY = (target.Height - actualY) / 2;

        return Matrix.CreateTranslation(offset.X, offset.Y, 0)
            * Matrix.CreateScale(scale, scale, 1)
            * Matrix.CreateTranslation(offsetX, offsetY, 0);
    }

    public Rectangle ClipLetterbox(Resolution target)
    {
        var targetX = Width;
        var targetY = Height;

        var scaleX = target.Width / targetX;
        var scaleY = target.Height / targetY;

        var actualX = scaleX * targetX;
        var actualY = scaleY * targetY;

        var offsetX = (target.Width - actualX) / 2;
        var offsetY = (target.Height - actualY) / 2;

        return new Rectangle(
            offsetX,
            offsetY,
            target.Width - offsetX * 2,
            target.Height - offsetY * 2
        );
    }

}