参考:C# .NET CoreでSystem.Drawingを使う方法
System.Drawing.Bitmap bmp = new System.Drawing.Bitmap(fileName);
var property = bmp.PropertyItems.Where(x => x.Type == 2 && x.Id == 0x9003).FirstOrDefault();
if (property != null)
{
string dateStr = Encoding.ASCII.GetString(property.Value).Substring(0, 19);
DateTime date = DateTime.ParseExact(dateStr, "yyyy:MM:dd HH:mm:ss", null);
}