EDIT: I'm sorry, I only just realized that "hostel" in Europe means something entirely different from "hostel" in the US. What I mean by "hostel", per how we use this term in Poland, is a cheaper version of a hotel, where you still rent by the room, and rooms are usually 1, 2, and 3-5 people-sized, and usually have kitchen and a bathroom in the room. They're not like dorms, they don't involve shared bunk beds. I don't know what the right term in the US is. Bed&Breakfast?
In principle, hostels have everything. A fridge, a kitchen and so on. In practice, though, you have to label all your food because there is one fridge for 50 people. You need to share the kitchen with everyone else too. Privacy is limited. Noise is biblical. Fucking party dickhead bros everywhere ruining everything. Creaky floorboards and noisy doors. I've done hostels all over Europe, and while there are exceptions, the exceptions tend to cost a bit more too.
Hostels are OK when you're young and broke and very adaptable. I used them a lot, and am grateful they exist. But they do NOT fulfill what the GP is asking about.
If it says "we have a great atmosphere, and go clubbing every night" it's a party hostel.
If it says "we have family and dorm rooms, kitchens and car parking" it's probably for families or school trips.
There are also hostels used by people who are essentially homeless, though I've never seen one advertised. I knew someone who volunteered at one.
On hotels.com, what you're looking for is described as an "apart-hotel".
Somebody mentioned extended-stay hotels elsewhere as the closest analog in the US, but they tend to be focused on business travelers, and not always located in tourist areas. For example, there are a ton of extended-stay hotels near my office, but that's 30 miles outside Washington DC in the heart of the northern VA internet/tech zone (AWS, Google, the remnants of AOL, etc).
Edit - I'm looking at Hotels.com now, searching Inverness UK from the US site. "apart-hotel" is not an option under "Accommodation Type". Apartment is a distinct type from hotel, and it appears to be a mix of what you describe (bocks of apartments managed for vacation lets) and individual apartments (Airbnb-style).
Edinburgh has some.
https://www.adagio-city.com/gb/home/ has many across Europe (also listed on hotels.com).
(Curiously, the Talk page of that article suggests that Polish law doesn't even recognize the term "hostel", so all those places - both defined here and the kinds I stayed in - must really be something else.)
Not in America. You might find a few in & near major cities, but hotels and motels are everywhere, bed & breakfasts are fairly common, and AirBnBs are plentiful.
I haven't personally stayed in one, because I have enough money that I'd never have to, but the impression I have is that one would contain a bed, a desk, a chair, a not-entirely-spotless bathroom, and not much else.
The quality varies from pretty tired and not so clean, as you say, to--if not upscale exactly--to comfortable, modern, and clean.
However, I can quite assure you that here in rural Upstate New York (and, indeed, even in some of the less-well-off sections of the cities), there are still a great many motels that date to the era I mentioned—very visibly so. (This is why I qualified my statement with "at least around here".)
I have actually stayed in Travelodges a couple of times, and while they were modern, I wouldn't really describe them as "comfortable" (the beds were like tandem canoes) or "clean", at least not universally so.
But, yes, there are also still quite a few non-chains or small chains that aren't... great.
Hostel in Ireland and UK invariably means cheap shared accommodation for young people, with facilities in common areas.
But yeah, if you want to cook, the options are slimmer. There ARE still options -- Extended Stay America, in the US, for example -- but mostly you'd be better off renting a property and not a hotel room.
Exactly, every business hotel I've ever seen has had a fridge, kitchen-style sink and a microwave. Then touristy locations often have condo rentals on a weekly basis which will have proper kitchens and washer & dryer, if you're travelling long enough to need a kitchen it's probably going to be a week or more.
Worst case people can do what Americans have been doing for decades, travel with a cooler and refill with new ice as needed. We did this all throughout my childhood when we'd go to Florida from Indiana, we'd eat out for dinner and sometimes for breakfast the whole trip but lunch was pretty much always sandwiches made from perishables kept in a cooler. We'd keep drinks in a small igloo and then we'd usually buy a large Styrofoam cooler for the food.
Not really my experience although a small refrigerator that isn't a minibar is more common than it used to be. Outside of extended stay hotels though, I don't see a microwave or other kitchen-related features very often.
Even something as simple as a fridge with usable space, not packed with minibar stuff, is hard to find. Hotels aren't very comfortable places to stay.