Yes misfire on cylinder 2 injector they said. I guess if this is not historic as my mechanic thinks then itilain tune, injector/carbon cleaning, will not help? The Vagcom guy said replacing the injector alone wouldn't solve it as needed new turbo too.
If it was misfiring would it run smooth through every gear with no hesitation or misfire besides the initial bogging?
It's just passed its mot too so emissions all good
Injectors are mechanical devices and can therefore misbehave intermittently. The pintles get gummed up and lazy. It could just be a particular temperature and duty cycle they're not happy at. These engines never misfire if all is well. Misfires severe enough to flag a fault (it has to miss several times for that happen) it's certainly a clue. I had an intermittent misfire on mine on cyl 3 at approx 90K miles which was a bad injector. I just put another set of 4 in and it's never missed since, not once.
I'm not suggesting it's them 100% because you can't be certain over the internet, but at your mileage and the symptoms, they can't be outruled.
Unless the turbo has bad shaft wear (wobbly turbine wheel) I really wouldn't go there with that. Focus on the cheaper, more fundamental issues first is my advice. The turbo should be the last thing on the list as it's very expensive and they either work or they don't, kind of like a light switch.
I would give it several hard runs over a week and see what that achieves and go from there. These engines really don't like short journeys. Well, they can do them, but they prefer to get a lot of air through them and heat to blow the cobwebs away.
Coilpacks and plugs recent/good?
When my injector went, it didn't feel rough, just very flat and unwilling to rev. The only clue was an occasional lumpy idle when hot.