On Earth there was furthermore a nasty nuclear war and I doubt that the population size is larger than today. It is probably smaller.
It has a population in the billions by First Contact.
And the casualties from World War III were in the 100 millions so it didn't kill the majority of the population.
For the first note:
Data: Population 9 billion, all borg.
That indicates the population with the Borg in full control, in a timeline where no wars post World War III took place, beyond replaced drones. This does not affect the normal/restored timeline population.
For the World War III reference:
I think Riker said something about 100 Million dead from World War III, and there was no indication as to the pre-war total population levels.
This means we have no way to tell how devastation WW III is, or how much an increase in population took place between 2063 and the mid-late 24th Century.