I’d go with the manufacturers recommendations but if your bench is suitable you could extend it closer whilst maintaining the gap with the cabinets.

Doesn't sound right, i would question it. I would also check with the cabinet maker if they recommend extra heat protection.

Just realised, we put a vertical metal strip to protect the cabinets from the opening oven heat but on top, the stone is snug against the stove.

I would definitely adhere to the manufacturers recommendations

I agree with big reader: always go with the manufacturer's recommendations for installation & speak with the supplier to see if they can recommend if the gap can be sealed.