Just listened to the audio clip - sounds like the usual HPFP / injector noise that most of them seem to have.
Now, obviously it's difficult to isolate and investigate a noise from an audio clip over the internet - and no one would not want you to fail to do essential repairs - but I would get a second opinion from someone who has a lot of experience of these notoriously noisy engines, before I set out on PiTY / expensive job.
Just a thought.