When quartz first came out, there were also several issues with quartz "ghosting" or scorching where a hot pot was set on it. Too many people took "heat resistant" to mean "heat proof". "Ghosting" is where the resin in the man made stone is slightly damaged by the heat, but not enough to scorch. It's a barely perceptible change in the appearance.

The bottom line is that pot holders, cutting boards and trivets (and fire extinguishers) should be a part of your ingrained everyday safety routine use in a kitchen and there honestly is zero need for anyone to either cut on a counter or to set hot things on it. While you certainly want a durable surface, that's a totally bogus requirement for a counter material.

However, in an emergency situation, if you had to dump off a super hot skillet off of the stove, probably only soapstone or copper, or stainless would have the chance to remain undamaged. And I say probably copper or stainless because if the item is hot enough, both can scorch and metal has a wood substrate that can certainly be damaged with enough prolonged exposure to heat.

I had an emergency situation in my first apartment kitchen where I forgot about a skillet of oil I was heating, but got to it before a fire resulted. I dumped it into my stainless sink. It scorched the stainless and melted the PVC pipe (and totally burnt the paint on the exterior of the cheap skillet!) I had to replace both, as the metal was permanently discolored despite me running cold water almost immediately after I dumped the skillet. Don't ever do that either! The correct safety procedure is to just move it to another burner and cover it with an oversize lid until it cools down. The resulting steam flash was almost as dangerous as the smoking hot pot itself.

The principle I keep in mind (for when I'm too lazy to get the cooling rack out) is thermal mass. That is, how much heat energy does the item contain?

A heavy cast iron dutch oven full of stew bubbling at 375F for a total weight of 20 pounds carries some serious thermal mass and would pose a big risk in my mind. The risk is that something with that much thermal mass has the potential to significantly raise the temperature of the granite underneath to a significant depth and by a significant amount, inducing heat stress with the cooler adjacent granite.

A toaster-oven tray with a slice of leftover pizza seems like a non-issue. Cookie trays with cinnabons, meh, I drop those right on the granite. But a 10 pound roasting pan of braised pork belly that's just been browned under the broiler at 450F, that always get a cooling rack.

Just imho, exercise your own best judgment.

Just don't do it. Not worth it. Get a trivet. And "heat resistant" means nothing.

so far now, several stories of granite cracking but not yet any stories of marble cracking! I know they must be out there ...

I have two large cutting boards that I pull when taking things off the stove or from the oven. Or I pulled them all the way out onto the counter to set electric appliances. I've had silestone or granite for amost 15 years in 2 homes, and never had any issues of any kind.

I won't even put the slow cooker (crock pot) on stone. He sits on the cooktop when he is in use.

Here's the griddle on Amazon with actual lefse on it
lefse griddle. For those who aren't familiar with this, think norwegian potato based tortilla.

Holly's cracking the pastry board pretty much answers the quetion too.