"Let's drive around the hood to flex my Mercedes Sprinter", said noone ever.

These are strictly professional cars. When they are not "in duty" they're probably parked at a garage.

On the other hand, an American open truck driving/parked in a residential area is almost certainly some show-off.

You misunderstand - almost every tradesman here drives their work vehicle home and drives errands in it. Use of the company vehicle for commuting is considered a standard perk of these trades for regular employees - free fuel (fuel is way more expensive here), they can some days drive straight to the first customer (saves time), and might save them from getting a car (maybe the spouse has a microcar for their commute, otherwise biking and public transport are common).

Source: I live here and see it every day. Family, friends and customers are doing it, plus many eons ago I too was a tradesman driving home every day in the company work van.

(Heck, many companies wouldn't even have a place to park all their company cars at once, many such smaller companies run out of regular residential buildings with no dedicated parking.)

Good point; I should actually make sure to pay attention rather than reading "Sprinters are bigger" and applying that to my hatred of American trucks!