What would an investigator be looking for?
We have an apparently quite talented and multiple-qualified (PPL, CPL/IR) experienced pilot in good weather flying an aircraft with which he is very familiar.
If the airframe was intact up to the impact he should have handled an engine failure from 3000' quite well. However there is the mention by a policeman attending the crash site that some part of the aircraft fell "many hundreds of metres away". What part was that?
If that story proves untrue, is it possible the pilot has been incapacitated? Either by engine fumes, or some internal (to him) sudden physiological trauma. I presume the investigators will be able to access the pilot's medical history.
It's extremely sad and as long as the cause is unclear anyone in the pilot's age group, fueling where he fueled, getting maintained where he was, or anyone flying the type should have cause for concern.