HI there MichalM !
starting to say that not being an expert in the mather but with some experience in informatic car diagnose , not just multi ecu but also vagcom opcom and scantool ; i realise something , there are specialised diagnostic software that are exclusive for a manufacturer like is the case of
MES for fiat group, vagcom for volkswagen group , opcom for GM group... and there are general diagnostic software like the scantool that can diagnose every manufaturer that complys with ISO rules ! so , what is the diference ?! with the general software i diagnose every one , why to buy one for every manufacturer ?!!
the diference is that the manufacturers are oblied by law to comply with the ISO protocols but they create specific fault codes of their ones besides the general ones that a general non specific software would not read !!
and this is allways evoluting ...
Resuming . do you noow wath software your mecanic used ?
if he used a specific software and found nothing wrong , probably the problem is not in engine it self like you suspect , if he used a general purpose and the lambda sensor is not broken but just defective there is a chance that poped out another specific fault and he couldent read it !?
note that i'm just guessing
you say the videos you posted there was no fault codes , because the MIL ligth was off ??
not all the fault codes triger the MIL !
It's not easy , there are issues and malfunctions very complicated even for expirienced mecanics that work in the oficial dealer and have acess to all information and tools .
My point is that a diagnostic tool is really very usefull in our days , every mecanic has one !!
And please keep posting the evolution of your problem , i'm learning to