Some observations...
Unless "they" used flexible tubing to pipe (?) connectors, separating the burner top from the oven would involve pivoting the stove top at the rear.
Can you see "anything" by taking the burner grills off and somehow wedging a small mirror and aim a flashlight to light up the area to see the burner manifolds?
Adjacent cupboards have no screws to fix the entire unit in place? I sure would look underneath looking up.
It is very likely nothing can be done until the entire unit is removed, which will expose hidden screws.