Exhaust Back Pressure Sensor Issue

That definitely sounds like it could be the exhaust back pressure sensor. That sensor measures the pressure in the exhaust system. This data is used by the engine control unit (ECU) to optimize engine performance and manage emissions. A faulty sensor can cause all sorts of problems, including incorrect fuel mixture, leading to smoke, and triggering warning lights. Have you noticed any changes in fuel economy or engine performance besides the smoke and light?

No noticeable changes in fuel economy or engine performance, other than the symptoms already mentioned. Is there a way to confirm it's definitely the sensor before I start replacing parts?

Without diagnostic equipment, it's tough to say definitively. However, the symptoms you describe strongly point to the exhaust back pressure sensor. The ECU is likely detecting an abnormal reading and triggering the warning light. Given the smoke on acceleration, the ECU might not be correctly adjusting the air/fuel mixture. To avoid misdiagnosis and potential additional damage, I'd recommend taking it to a trusted mechanic. They can use a scan tool to read the sensor's output and confirm if it's faulty.

Thanks for the advice. I took it to the shop, and you were right it was the exhaust back pressure sensor. Cost me 245€ to replace. Running smoothly now.