2004 VW GTI P0343 Code: Cam Position Sensor Issue and Troubleshooting Guide

I own a 2004 Volkswagen GTI with a 1.8L turbo engine. The vehicle has been displaying a Check Engine Light with fault code P0343, indicating a camshaft position sensor issue. I've verified the voltage and ground connections at the sensor connector—both are within specifications. After replacing the camshaft position sensor with a new one and clearing the code, the P0343 error reappears within minutes. All wiring appears intact, and I’ve also tested the crankshaft position sensor, which shows no issues. The previous owner replaced the timing belt before I acquired the vehicle, so I've double-checked that all timing marks are properly aligned—everything looks correct. The engine starts smoothly but runs with a rough idle, especially at low speeds, though it performs normally above idle. Any advice on further diagnostics or potential causes for this recurring P0343 code would be greatly appreciated.