Thanks to everyone for your help! Special thanks to Jim Mischel for pointing me in the right direction.

In WPF, there's a handy method called PointToScreen that helped me solve the issue. This method converts a point relative to a WPF element to screen coordinates, which was exactly what I needed.

using System;
using System.Drawing; // For screen capturing (Bitmap, Graphics)
using System.IO;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Input;

namespace ScreenCapture
{
    public partial class MainWindow : Window
    {
        private System.Windows.Shapes.Rectangle DragRectangle = null; // Specify WPF Rectangle
        private System.Windows.Point StartPoint, LastPoint;

        public MainWindow()
        {
            InitializeComponent();
        }

        private void Window_PreviewKeyDown(object sender, KeyEventArgs e)
        {
            if (e.Key == Key.Escape) { this.Close(); e.Handled = true; }
        }

        private void canvas_MouseDown(object sender, MouseButtonEventArgs e)
        {
            StartPoint = Mouse.GetPosition(canvas);
            LastPoint = StartPoint;

            // Initialize and style the rectangle
            DragRectangle = new System.Windows.Shapes.Rectangle
            {
                Width = 1,
                Height = 1,
                Stroke = System.Windows.Media.Brushes.Red,
                StrokeThickness = 1,
                Cursor = Cursors.Cross
            };

            // Add the rectangle to the canvas
            canvas.Children.Add(DragRectangle);
            Canvas.SetLeft(DragRectangle, StartPoint.X);
            Canvas.SetTop(DragRectangle, StartPoint.Y);

            // Attach the mouse move and mouse up events
            canvas.MouseMove += canvas_MouseMove;
            canvas.MouseUp += canvas_MouseUp;
            canvas.CaptureMouse();
        }

        private void canvas_MouseMove(object sender, MouseEventArgs e)
        {
            if (DragRectangle == null) return;

            // Update LastPoint to current mouse position
            LastPoint = Mouse.GetPosition(canvas);

            // Update rectangle dimensions and position
            DragRectangle.Width = Math.Abs(LastPoint.X - StartPoint.X);
            DragRectangle.Height = Math.Abs(LastPoint.Y - StartPoint.Y);
            Canvas.SetLeft(DragRectangle, Math.Min(LastPoint.X, StartPoint.X));
            Canvas.SetTop(DragRectangle, Math.Min(LastPoint.Y, StartPoint.Y));
        }

        private void canvas_MouseUp(object sender, MouseButtonEventArgs e)
        {
            if (DragRectangle == null) return;

            // Release mouse capture and remove event handlers
            canvas.ReleaseMouseCapture();
            //canvas.MouseMove -= canvas_MouseMove;
            //canvas.MouseUp -= canvas_MouseUp;

            // Capture the screen area based on the selected rectangle
            CaptureScreen();

            // Clean up: remove rectangle from canvas
            canvas.Children.Remove(DragRectangle);
            DragRectangle = null;
            this.Close();
        }

        private void CaptureScreen()
        {
            // Convert StartPoint and LastPoint to screen coordinates
            var screenStart = PointToScreen(StartPoint);
            var screenEnd = PointToScreen(LastPoint);

            // Calculate the capture area dimensions and position
            int x = (int)Math.Min(screenStart.X, screenEnd.X);
            int y = (int)Math.Min(screenStart.Y, screenEnd.Y);
            int width = (int)Math.Abs(screenEnd.X - screenStart.X);
            int height = (int)Math.Abs(screenEnd.Y - screenStart.Y);

            // Ensure dimensions are valid before capture
            if (width > 0 && height > 0)
            {
                using (Bitmap bitmap = new Bitmap(width, height))
                {
                    using (Graphics g = Graphics.FromImage(bitmap))
                    {
                        // Capture the area of the screen based on converted coordinates
                        g.CopyFromScreen(x, y, 0, 0, new System.Drawing.Size(width, height));
                    }

                    // Save the captured image to the desktop
                    string desktopPath = Environment.GetFolderPath(Environment.SpecialFolder.Desktop);
                    //string filePath = System.IO.Path.Combine(desktopPath, $"Screenshot_{DateTime.Now:yyyyMMdd_HHmmss}.png");
                    string filePath = System.IO.Path.Combine(desktopPath, "Screenshot.png");
                    bitmap.Save(filePath);
                    System.Diagnostics.Process.Start(filePath);
                    //MessageBox.Show($"Screenshot saved to {filePath}");
                }
            }
        }
    }
}