Perhaps it is better to call it an overshoot. Is the w140 drive by wire? I believe my father’s w210 was, but it had a 606 engine.
You can see a few things on this cold start. It starts at about the right RPM (~750-850), but after any user interaction, it settles too low (~550). That final throttle blip is the best example. I gave it a little pedal and it kept going to over 3000. Once the engine is warmer it doesn’t seem to do this.
https://youtu.be/MXt9yiNTHdY
What in there might be sluggish?
The engine is very clean, and I lubed the throttle points I could.