Kia Soul 2011 2.0L idles high. Then after warming up drops to a rhythmic revving up and down 1400-1800rmp

Question

I just bought the car at auction. Was driving fine. It started 20 minutes later. Error codes P0121, P0507, P0441.
Car likely was sitting for months before I bought it.  I cleaned the throttle body and replaced the throttle position sensor to no avail.  I did notice at cold start some white smoke coming from the upper O2 sensor area.

Answer 1

Maybe a leaking exhaust manifold. Does the engine sound louder than normal on cold start? Is there any exhaust smell from the engine area?

When exhaust manifold leaks, it causes the engine to run rich.

To check if exhaust is leaking. Remove the heat shield over the exhaust manifold. Start the engine and while it is still fairly cold, run your hand just above the manifolds. Should be able to feel it. Other options are a smoke machine typically used for finding EVAP leaks. Or pressurizing with compressed air and using soap bubbles.