There is a specific word that describes the stairs before the door like in the picture here.
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I call them "front steps". I live in Seattle.
My grandparents from Chicago would have called them a "front stoop".
My impression is that they are called a "stoop" in areas where row houses are common in big cities. This might be a coincidence: Etymonline says that this meaning of the word "stoop" is derived from Dutch. New York City was originally settled by the Dutch, and is at the center of the North American "areas where row houses are common in big cities."
In the UK "steps" or "front steps". In the UK a 'door step' is the single step up in front of a door (possibly two) - not steps in a flight such as these. They would not be called stairs. We also do not use 'stoops' in the UK.
Some of us would call it a "stoop" or a "front stoop," as in the third definition here. That may vary by region in the U.S., but it is said in New England, at least.