With a couple of exceptions, it's fairly straightforward. Is it recognized as a sovereign nation by the UN, does it issue passports, does it control import and export of goods, does it enter into international treaties?
Yes, I know we have people in Arizona who claim to be sovereign and people in places like Texas who want to become their own nation. Thing is, it's only in their view, no external authority recognizes that.
You are assuming "country" and "sovereign state" are synonyms, but that isn't true in general. The word "country" is used to refer to the four first-level subdivisions of the UK - England, Scotland, Northern Ireland and Wales - this is standard and well-established English usage (well, certainly standard British English). The concept of a sovereign state having subdivisions known as "countries" is not unique to the UK, as the following article attests - https://en.wikipedia.org/wiki/Constituent_country
Scotland in particular is one of those exceptions.
There really is no one magic rule that says 'country vs no country' - even what you offered up is a collection of rules, where some rules catch edge cases that other rules don't.
I'm thinking more exceptions where military might and economic might are immediate threats whereas that's not the case most people would concede about Scotland.
Yes, I know we have people in Arizona who claim to be sovereign and people in places like Texas who want to become their own nation. Thing is, it's only in their view, no external authority recognizes that.