You're supposed to use the Visual Studio Image Service and Catalog. However this document doesn't explain how to get the image for a given file.

You'll have to use the IVsImageService2.GetImageMonikerForFile Method. As described in the document, you can get GDI/Winforms, Win32 or WPF images. Here is a sample code that does it for WPF's BitmapSource:

public static async Task<BitmapSource> GetWpfImageForFileAsync(AsyncPackage package, string filename, int width, int height)
{
    if (package == null)
        throw new ArgumentNullException(nameof(package));

    var svc = (IVsImageService2)await package.GetServiceAsync(typeof(SVsImageService));
    if (svc == null)
        return null;

    var mk = svc.GetImageMonikerForFile(filename);
    var atts = new ImageAttributes
    {
        StructSize = Marshal.SizeOf(typeof(ImageAttributes)),
        Format = (uint)_UIDataFormat.DF_WPF,
        LogicalHeight = width,
        LogicalWidth = height,
        Flags = (uint)_ImageAttributesFlags.IAF_RequiredFlags,
        ImageType = (uint)_UIImageType.IT_Bitmap
    };

    var obj = svc.GetImage(mk, atts);
    if (obj == null)
        return null;

    obj.get_Data(out object data);
    return (BitmapSource)data;
}

Here is how you can use it for example at package initialization:

public static async Task InitializeAsync(AsyncPackage package)
{
    ThreadHelper.ThrowIfNotOnUIThread();

    // note a valid extension is sufficient
    _pngBitmap = await GetWpfImageForFileAsync(package, "whatever.png", 32, 32);

   // etc...
}