'The Cambridge Guide to English Usage’ has this to say on the matter:
Noun phrases that act as quantifiers can take either singular or
plural agreement . . . As elsewhere when there are agreement options,
the singular verb seems to invoke the set, whereas the plural verb
makes us aware of the individual items in it.
What this means for your example is that you should use the singular verb, as you have in the first sentence, if you want to emphasise the rest of the world as a unified mass, but the plural verb if you want to emphasise the fact that it is made up of individual people.