What is the finish? Enamel?
Enamel doesn't scratch easy, unless sand is present, but it does chip.
You could always put a cast iron trivet on top and cook from that. Just be careful not to slide it around while maneuvering the pan/pot.
As long as you pick straight up/down you shouldn't be in much danger of scratching it...but if you stir aggressively you might.
That looks like cast iron stove or like you said stove paint. Cast iron on cast iron the weaker of the two shall scratch or both.
I have seen a granite block used on an old stove before. Looked like that block had been with that stove for years. The block looked very used and they had nice iron skillets on it while I was there. That stove was original to the house and that house was built in 1919. I would say that block was as old.
I would get a restaurant quality stone like a fibrament stone. The ones like Pampered Chef sells break pretty easily when used with hot temps.
The OG is familiar with the granite, so that is my next search.
Have you tried calling the manufacturer to ask? My grandparents do a kettle on theirs without and issue but not cooking in pans or anything.
Rep inbound for a sensible observation.
Stove polish like patience0830 recommended is what we used when I was growing up.