The k-pg extinction was instant in a geologic sense, but in terms of individual animals it felt more like a slow decline. It took a few thousand years for the whole thing to happen[1]. With effects lasting into the 500,000 year range.
For most birds the air pollution was similar to what you see from large forest fires. Even when skies were orange in San Francisco a few years ago, birds weren't dropping dead. High AQI kills slowly, if you (or a bird) are not inhaling smoke directly.
But yes every bird within a few thousand kilometers of the impact site probably died instantly. Most birds and other animals were not within that radius.
[1] https://en.wikipedia.org/wiki/Cretaceous%E2%80%93Paleogene_e...
I wonder if far in the future the cockroach or perhaps ant-colony wikipedia will say something like:
"The sedimentation rate and thickness of Anthropocene-Insectocene clay from three sites suggest rapid extinction, perhaps over a period of less than 10,000 years."
... though it doesn't get into the air quality directly.