ArtificialStackTraceException.cs

public class ArtificialStackTraceException : Exception
{
    public ArtificialStackTraceException(
        bool shouldIncludeFileInfo = true,
        string message = "Artificial exception used to generate a stack trace."
    ) : base(message)
    {
        var stackTrace = new System.Diagnostics.StackTrace(shouldIncludeFileInfo);
        StackTrace = stackTrace.ToString();
    }

    public override string StackTrace { get; }

    public override string ToString()
    {
        return $"{nameof(ArtificialStackTraceException)}:{Environment.NewLine}{StackTrace}";
    }
}

ArtificialStackTraceExceptionTest.linq

<Query Kind="Program" />

public class ArtificialStackTraceException : Exception
{
    public ArtificialStackTraceException(
        bool shouldIncludeFileInfo = true,
        string message = "Artificial exception used to generate a stack trace."
    ) : base(message)
    {
        var stackTrace = new System.Diagnostics.StackTrace(shouldIncludeFileInfo);
        StackTrace = stackTrace.ToString();
    }

    public override string StackTrace { get; }

    public override string ToString()
    {
        return $"{nameof(ArtificialStackTraceException)}:{Environment.NewLine}{StackTrace}";
    }
}

void Main()
{
    new XElement("LINQPad.HTML", new XElement("h3", "new Exception")).Dump();
    Foo(() => new Exception()).ToString().Dump();

    new XElement("LINQPad.HTML", new XElement("h3", "Try...catch")).Dump();
    Foo(() =>
    {
        try
        {
            throw new Exception();
        }
        catch (Exception ex)
        {
            return ex;
        }
    }).ToString().Dump();

    new XElement("LINQPad.HTML", new XElement("h3", "new ArtificialStackTraceException")).Dump();
    Foo(() => new ArtificialStackTraceException()).ToString().Dump();
}

Exception Foo(Func<Exception> generateException)
{
    return Bar(generateException);
}

Exception Bar(Func<Exception> generateException)
{
    return Baz(generateException);
}

Exception Baz(Func<Exception> generateException)
{
    return generateException();
}