> Adding those two populations together would seem to indicate that most Western populations are already at herd immunity by this point

That's assuming that nobody who got covid later got vaccinated (or got it before the vaccine kicked in). That seems like a very unrealistic assumption to me. On the other side, there are probably a lot more cases than are reported.

You're right that it almost certainly matters for heard immunity, but i think you need a much more complex model to know how much of an effect it has.