I would suggest HP diesel fuel pump Stephen! Car seems to accelerate well and probably smooth in power delivery. Sound is very distinct and clear to anyone with half an ear and it is too easy for garages to say they don't know what it is. It's their job to find out! If they genuinely don't know, they should pass your excellent video/audio clip to Audi Technical Services for their professional judgement.so they will recognise the problem and be able to fix it for other customers too.
Garage technical work has been deskilled to the extent that no one knows the cause of any problem unless 'diagnostics' say so. Conditions arising through wear of components etc are therefore not usually picked up by diagnostics and the technicians are unable to go back to basic principles and work things out. Suggest you ask garage how they propose to proceed with diagnosing your problem as it definitely needs attention, or monitoring if they assure you that it is OK to run with the condition.
