I feel like “darts” is the odd item out in this list of (presumably) Americana.
In any case, a gentle reminder that the USA has hundreds of missiles carrying nuclear warheads ready to launch…
…and that the President of the United States has virtually unrestricted nuclear launch authority.
I don't think Quark is naming American things, he's naming Earth things, and all he knows is stuff Bashir, Sisko, and O'Brien have shown him, which includes darts.
(Sulu is from San Francisco. Kim codes Asian-American very hard. Sato is from Japan. We don't see an Asian from Asia as a major character until I think Georgiou on Discovery? One or two South Asian characters.)
I think it is implied Starfleet headquarters is where it is because it's one of the few major cities that wasn't destroyed (along with Paris apparently?).
I wonder if SF was/is a hardship posting for Vulcans. You've got to think that was a lousy place to live, especially in the pre-TOS era when the environmental tech wasn't there.
If I recall, the original timeline had WWIII start with a conflict between a Chinese lead alliance and a renamed EU, with the Eugenics war being a separate earlier thing, but I think Picard changed that to them being either the same thing or concurrent? Haven't watched S2 or 3 of Picard.