Lexus is300 2019 p0303 and p11ee error codes

I have a misfire on Cylinder 3 (P0303) and an air-fuel code (P11EE). I’ve already tried new spark plugs and swapped the ignition coils around, but the misfire stayed on Cylinder 3. I took the car to Lexus for the diagnostic test but they couldn’t diagnose the problem and wanted to do a compression and leak down test for $800 and that’s when I decided to go to a independent shop.

One specific detail: The car turns on perfectly with no hesitation, but the shaking starts about 10-15 seconds after starting. It shudders in Drive and Reverse, but once I’m moving, the drive feels normal.

The car is currently at 83k miles with the CEL. The light came on after sitting outside in the cold for one night when it’s typically in the garage.

What could this be? Feel free to ask any questions or give your opinion!