For example, “Washington” (US), “Brussels” (EU), “Moscow” (Russia).
I guess it’s a short hand for writing “US government”, “Russian government”, etc. but why? And what happens when you’re referring to a country with multiple capitals like South Africa?
Yes, it’s metonymy, as people have said. You also get it in similar contexts where people will name a building such as ‘the White House’ or ‘[10] Downing Street’ to refer to the governments of the US or the UK.
Or specifically the parts of government that reside there. I see it especially used when there may be dissent in other parts of government.
Yes, very useful for subtle distinctions like this!