Yes, specifically focusing on birds. That is the focus I usually see when cat hunting comes up online.

It makes sense small animals that can’t fly would be easier prey - and therefore more likely to be impacted by predation - but I guess only birds are cute or something.

Cats kill huge numbers of birds. Most small bird species have high reproduction rates, and crowding results in higher death rates from increased disease and parasite spread, competition for food, and all the good shelter from predators being taken. Higher death rates from one cause (say, cats) results in less death rates from crowding-related causes. I haven’t seen any evidence that, in general, cat hunting ends up actually impacting bird populations.

Specific species of birds in certain locations have been harmed by cats: the Wikipedia page list several examples in Australia (https://en.m.wikipedia.org/wiki/Cat_predation_on_wildlife). So it’s good to have local awareness if there’s a particular vulnerable population. But in general, keeping cats inside is only for their own safety and won’t impact bird population one way or another.

It may not be abstractly good for cats to be allowed outdoors (my family growing up had a cat eaten by the neighbors dogs, a cat get hit by a car, multiple cats get serious injuries from fights with neighborhood cats, etc.) But having been in a household with a series of cats that only went out when they asked to be let out: they ask to be let out every day. It is completely inconsistent with my experience that a cat would “never want to go outside again”.