It sounds similar to what I experienced with my A4 2.5 V6 TDI, manufactured in 1998 with 150 horsepower, especially when the engine is cold.
absolutely nothing, roughly from 80-90 degrees, and then it's just absolutely terrible

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It smells strongly of burnt oil, and the smoke disappears when you start driving.
Solution: A filter is installed in the crankcase ventilation system (a part that costs €30), which is connected to...
As the engine ages, the crankcase pressure increases, leading to oil leaks at the engine seals and resulting in smoke. In the worst-case scenario, the crankshaft oil seal can even be forced out.
There's nothing you can do yourself; the filter is located under the pump and turbocharger

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For me, everything was fixed immediately after replacing the filter, including the oil consumption.
It ended up being around 1 liter per 6,000 kilometers for me.
Greetings.