The Royal Navy still existed on 22nd century Earth, so even the British royal family are still around.
A DS 9 novel mentions the President of the USA touring San Francisco, after the Breen attack on Earth. Nation states still exist on Earth, the U.E government sounds like the United Nations but with more teeth and political power. It is probably a federalised form of government. Humans learn the hard way to work together after WWIII and First contact. Nation states stop seeing each other as political enemies. There is no 'Superpower' or 'Leader of the free world', no political dictatorships or extreme religious theocracies. (Islam would have to reform BIG time, as Christianity did in the past).
E. g Chekov is a very proud Russian; positive cultural national pride is still around, and so it should be. I would hate to think the rest of the world becomes a carbon copy USA.