As an example (the example that sparked this question), according to Wikipedia, the Seoul National Capital Area contains about 48.2% of South Korea’s population. That seems pretty high, but what’s the highest?
I realize this depends on the definition of metro area. I don’t really have one in mind, so feel free to cite anything.
Originally I was going to mention Vaduz, Liechtenstein (which technically isn’t a city-state) but apparently the city has only 15% of the country’s population.
Another contender would be Djibouti, capital of the Republic of Djibouti. City/country populations are estimated at 624k / 864k respectively, though there seem to be several different numbers running around Wikipedia.