Those places you're looking for are called hostels. They're cheaper and there's likely more of them than hotels in any given place. They're also legal and don't break the social contract.
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.
I made an edit in my comment. Must be a US/Europe term difference. I don't know what the horror show you described is called in my part of Europe, but over here, hostels have nothing to do with shared fridge for 50 people, or limited privacy. They're just cheaper hotels. Kind of like a motel, except not optimized for cars, and usually in an apartment building.
Hmmm, unless things have changed since I backpacked western Europe, hostels in London|Barcelona|Florence|Paris are dorm-style with shared bathrooms and other facilities. So, it's not a "Europe" thing either. As a 40-something professional, I would never stay in a hostel - I'm too old for that crap. I want a nice bed, a small living room, and a small kitchen.
"apart-hotel" isn't really something that exists in the US. And I had no idea it was a searchable term in some online booking tools.
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).
Sometimes I stay at "apart'hotels" in Europe. At least at the chain I've used a number of times, it's really just a hotel with 1.) Some cooking facilities like an extended stay place in the US and 2.) Cleaning is just weekly. They also tend not to have features like bars and gyms that many hotels do. But, really, at least for my uses it's pretty much a hotel with a 24-hour front desk.
In a state of even greater surprise, I accept that the word "hostel" may in general mean something else than what I came to expect from staying in places calling themselves "hostels".
(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.)
People in the US would generally call them "Extended Stays" but they're usually as expensive as hotels but not necessarily located in places where you'd want to be. In my experience they're either in industrial suburbs or just off of a highway exit. They're targeted at people who will be away from home for more than a few days and/or where a hotel room is too small/ill equipped.
> and there's likely more of them than hotels in any given place.
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.
So what's the correct term for "a cheap hotel, usually without a minibar in the room"? Because that's what we call a "hostel" over where I live, and I assume in the rest of Europe.
Motel. They're usually what you'd expect from the lowest end of hotels, and (at least around here) a great many of them are left over from the '50s through the '70s—the pre-interstate era, where driving to visit somewhere several hours away usually meant stopping in some little town overnight.
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.
That's certainly the image that the "motel" term conjures up. TBH, I'm not sure how broadly the term is used any longer. There are certainly more modern hotels/motels, many of them big chains, that are designed around people driving to them so you can usually park near your room.
The quality varies from pretty tired and not so clean, as you say, to--if not upscale exactly--to comfortable, modern, and clean.
Oh, yes; there are certainly many chains like Travelodge and Motel 6 that fit the category of "motel" but are more 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.
I'm thinking more things like Comfort Inns or the lower-end Marriott brands. I'd put Travelodge and Motel 6 pretty near the bottom of the national chains. I had the misfortune to have to stay in a Travelodge last year because of a last minute trip.
But, yes, there are also still quite a few non-chains or small chains that aren't... great.
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?