Regarding the carbon on the shaft that you observed, it is indeed highly likely that the rear shaft seal was leaking Oil is very often overlooked as a critical component When the rear seal leaks, it allows hot exhaust gases from the turbine housing to enter the bearing housing
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This contamination can cause the oil to degrade rapidly, leading to sludging and coking
Here we explore some common causes of oil leaks and things to check if your turbo leaks oil.
Another way to identify the oil seal leaking is by letting the engine idle for a min or two and then pull away normally (engine under load) if seals are leaking there will be some blue/white smoke, which then clears This should tell you if the exhaust side oil seal is knackered.
