LVT would get my vote. Easy to clean and you can use a steam mop on it too.

Ask your self if the kitchen is actually a good kitchen….. if you need a utility room next to the kitchen for additional refrigeration or storage or additional work surface then it’s not a good enough kitchen for you. Ideally the utility should be just a laundry room in which case it’s best near the bedrooms upstairs or at least near the bottom of the stairs.

oh old post to practice, the obvious choice is first floor extention but this only if the ground foundation on the back supports for this floor. Its mirroring the outer wall of the ground floor so enough area, there also alternative option of cantilever steel beams or concrete floor slab for first floor side extention though maybe need additional permit . Bedroom 3 will slightly Bigger than original, Plan A Plan B - Very Narrow Hallway Plan C - With Cantilever

I'd also be inclined to swap them as Jonathan suggested. Check fire regulations, as perhaps you do need to rotate the stairs to allow an open kitchen. (I'm in the Netherlands so can't advise on these.)