Questionable diagnosis of a workshop

Meal, I briefly describe my “problem” here. I currently have my car in a workshop far away from my home town. There the VSD should be changed, which is also fulfilled however the communication is quite poor and unprofessional (don’t report as discussed etc.). Now comes the workshop informs me that my control chain is hung, do this by sending a video as someone shakes with the finger on the steering chain and this The workshop suggested engine out and chain changes for the 3000-4000 € extra. My car has no typical signs which point to an elongated control chain (rash, ruckel, lamps gleam etc.). Due to this imense calculation is for me now questionable to what extent this diagnosis is “reliable” or if here is only trying to press the bill a little bit if you are already there. Thanks already