The owner left the car with us for a check first. After that first look, the owner went ahead with the full engine overhaul, and we went through the engine and the underside of the car.
We found several problems behind the oil loss.
Inside the engine, the piston rings were clogged. That was the reason the engine was burning oil.
The oil separator was not an original part. It was one of several oil leak points, along with the engine oil sump and oil level sensor, the valve cover and oil cap, and the oil pressure switch and control valve. The fuel injector O-rings had aged and hardened. The engine oil cooler had been patched with sealant at some point before. The automatic transmission was leaking oil too.
The timing covers deform once removed, so they had to be replaced.