Are you wondering if the correct SW is installed ? Dealer would be able to tell...
I suspect that if and when the Carbon Deposit cleaning was done it was not done fully or standard values not properly reset at the time.
Other than that don’t understand this shaking thing, if at or near idle only when cold points to Glow Plugs and or the Glow Plug Control Unit.
Mine does occasionally give a bit of very light what I’ll call coughing at about 1500 RPM and very light on the Gas. it’s definitely the EGR adjustment... Some time ago it was allowed to adjust to 0.7 but no more so I just have to live with it or shift a gear down. Again, hardly noticeable. In your case may just be the EGR setup as well...