Regarding the carbon on the shaft that you observed, it is indeed highly likely that the rear shaft seal was leaking 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 When the rear seal leaks, it allows hot exhaust gases from the turbine housing to enter the bearing housing
Turbocharger Oil Seal Leakage Explained - Page 2 - RX7Club.com
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.
Oil is very often overlooked as a critical component Turbo / turbocharger oil leaks can be caused by a variety of factors which often originate around the correct pressure within the compressor and turbine housing.