That looks like a coolant leak issue. You'd have metal specs if it was from the ledge. Here's an example from someone posting.
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You said you didn't observe losing much coolant, so you might be losing some. Doesn't take much to change the color of oil.
Take your old oil and put it in a clear cup. Check if it separates somewhat.
Changing the oil once would not remove all the gray oil from the engine block. You'd have to flush several times. Cheapest would be to check your oil filter housing gasket and then vanos solenoids if necessary before jumping to conclusions. Although I'm not sure how long you've been running you car like this, the vanos system might be very unhappy and you might actually have bearing wear.
Also, what operating temperature is the 2a82 showing up? Is it continually present or triggered once. You can view intake/exhaust camshaft advancement in INPA after replacing OFHG and flushing the system. Again, could be the contaminated oil impacting the vanos system.
I had a 2a98 code on cold engine start up every 200 or so miles. Replaced solenoids.