I think....no regarding the valvetronic motor or pin. You haven't said much more about the lazy motor?
The valvetronic learning process is just teaching the shaft it drives, where its start and finish point of travel is. A car electric window works in a similar way when it has a one touch function, it needs to know where top and bottom are.
If the motor is lazy I would expect if nothing else has been done with it, that the fault code for it may be back. I think they have to re-teach the motor as it may have to come off to get the rocker or cam cover off. If they don't then I don't know why they had to go through that process. The motor has a worm gear that drives a geared quadrant, which extends the lift of the inlet valves under varying load. If the motor is still lazy it may contribute to your symptom.
They need to ask themselves is the motor lazy? or is it being restricted by another component? Is there a clue in the stopping pin breaking? Is there a bigger clue in the broken teeth on the eccentric shaft I think it is called (the quadrant is part of it).
There can be other consequential problems here, including cylinder head I believe, as the shaft rotates in irreplaceable bearings which are part of the head, just as the camshafts do.
Factors include poor oil change frequency or incorrect oil type, and on the later engines which seem to consume a lot of it, running the car on low oil level, can accelerate a build up of, or cause residue that tightens components, causing stress, or accelerate wear. Low oil level simply makes the remaining oil work very hard to do its job, and the oil change interval doesn't get reduced knowing the oil has been low usually, it just gets topped up mostly.
If the interval is 20k for 4.5 litres roughly, it's just too long, let alone when low.
The garage may have to be considerate with hours spent, as they may have missed something. However..... and sorry...... it's your car, so wear affected parts you may just have to bear, and hope that things you can't see deeper in the engine, can be preserved by several oil flushes, and future maintenance adjustments perhaps, halving the oil change interval if not more.
The original discovery of leaked oil on the plugs and coils may be a partial explanation, or even a coincidence, and not all of the problem. It's not necessarily the garages fault other than if they missed something when the cover was off, but they couldn't fairly be expected to ignore the oil contamination, and look for what else might cause your symptoms. That wouldn't be fair to you or their reputation.
Only my 2p here, I hope I interpreted your post correctly
Authorise further work cautiously, and keep records accurate of what you have been told is the reason for what. Ask for old parts if required and photos of the internals you may be able to have explained to you later perhaps?