That seems like a very high bound. Another source says there are 7.2B birds in US and canada[1], so 1B birds would be 14% of all birds, which is really high. I also feel like 7.2B dead birds would be very noticeable in the form of dead birds on sidewalks, which I'm not seeing.
It might surprise you, but buildings in places other than the US and Canada now have windows too. By some estimates 95% of the world's windows are outside of US/CA!
(Not that it matters, birds are a pretext, nobody really cares about birds, otherwise outdoor cats as pets would not be a thing.)
The source linked in the parent post says the 1 billion figure is for US only. Maybe the number is more plausible if it's applied worldwide, but the source should be considered as unreliable.
(Not that it matters, birds are a pretext, nobody really cares about birds, otherwise outdoor cats as pets would not be a thing.)