the chain tensioner is fine as the chain is tight with no slack.or so I was informed
You take too much of what you are told for granted without question. If you have a hydraulic chain tensioner like the many reported to fail and give problems in V.Ws, how can anybody tell you a chain is tight when it's under the timing cover and only tensions the chain when the engine runs with oil pressure? There is only one way I know of, so ask your expert to tell you how he knows the tensioner is tight and working when the engine runs? If he doesn't give the answer at the end of my reply, he's not worth trusting.
As for the correlation, what figures would you like I am going by the fact that the ECU said that the 2 sensors don't match when everything is physically lined up.
You haven't understood that a fault code only tells you there's a fault and nothing more. You have to read the output from the cam angle sensors (in degrees) and understand what the results are telling you. Correlation means the degrees of cams are each within a close tolerance of each other and not offset or changing as the engine runs. V.W incorporate tolerances into values coming off sensors and when these are read outside a permitted range, a fault code is triggered either real because that's what's happening (evidenced by your poor idle), or a faulty sensor isn't giving a value the ECU expects. When you have two of something, V.W often compare values they expect to 'track'.
I've already suggested you look at camshaft timing controlling elements. I don't have your engine but fault find from first principle engineering, not Google, the internet or what somebody asks me to believe. I'm not saying a camshaft tensioner is your actual problem, that's for you to pursue and eliminate yourself, not just take what you have been told. But let's hypothetically consider the chain you can't see is running slack? Of course as I said it's the one thing if true that will destroy your engine which you must take out of the equation and be confident about. You seem good at reading the internet so plug in 'V.W timing chain tensioner' and ask yourself if you should have thought about it whilst replacing the chain? That's the difference between a competent V.W shop and your DIY attempts. You can use diagnostics to monitor the camshaft angle when the engine is running. Those figures can give some information about chain slackness or wear. AFIK that is the only way of measuring if something is wrong when the chain parts are hidden under the cover and running in oil.
What else is left I've not already mentioned? If one camshaft bearing is badly worn, the chain may be held tight but the shaft will run eccentric and angles measured by sensors will not correlate. I would expect to see small cyclical differences in camshaft angles varying at roughly half engine speed frequency? OBD tools are probably too slow to see this, but other tools connected directly to camshaft sensor outputs might show this better. I don't think you'll easily find this kind of innovative 'Outside the box' testing on the internet, or have the test equipment to do it.
If the VVT was suspect in the first instance, there are some tests which could have been done and diagnostics should have shown the camshaft advancing or retarding with rpm as further evidence of a fault or not before you swapped parts. But you both seem to want to change parts. Eventually you will be swapping the complete engine!
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