I would say that the word "city" has both a social and a legal aspect. From a social aspect, a "city" is an urban area, a place with many buildings and little green space except in parks. From a legal aspect, a city is whatever is inside the official city boundaries, which may include some area that is rural in aspect, and is not unlikely to include some area that is suburban.
I notice that the word "suburb" does not seem to get many mentions in this thread, but I think it is quite relevant.
Say I live in the urban area of a small city in "the middle of nowhere", ... can I say "I live in the countryside"?
You can say whatever you like, but if you live in an urban or semi-urban area, most people I know would badly misunderstand you when you say: "I live in the countryside".
To me "the countryside" refers to either a truly rural area, where either farms or undeveloped land predominates, or a semi-rural area, where residential uses predominate, but each home sits on a large plot, usually several acres or more. The word 'countryside" tends to suggest small roads with little traffic (except for occasional highways cutting through). It suggests areas with lots of trees or other vegetation, or crops, or in some areas relatively barren land with little vegetation but few artificial structures.
In a few places areas I might call "countryside" are legally part of a city, but this is rather rare.
The place I currently live is definitely suburban. Houses are single-family, and sit on anywhere from 1/4 acre to 2-3 acres each. But areas filled with office buildings are within walking distance, and a definitely urban area is within 15 minutes drive. I would not call this "the countryside".
I have lived in a municipality of about 25,000-30,000 population, that was largely suburban, with some small urban areas, and some definitely rural areas. It was not legally a city, but a township, but that was a matter history, other nearby similar jurisdictions were legally cities. Except for the areas that remain dedicated to farming, I would not call any of it "the countryside" but none of it is a dense urban area either. Neither of the pictures in the answer by Michael Harvey fit any of it at all well.
So based on the description in the question, I would not speak of the area as "countryside".