That depends on where you live. Every ecosystem is different.
Australia or USA? Yes thats bad.
Central Europe? Not so much.
The source is NABU = “Nature and Biodiversity Conservation Union” (the largest non-profit nature conservation organization in Germany)
Translated from german:
But you have to look at the overall picture: only in human settlement areas are cats a serious factor that can partially lead to a decline in bird populations. But in fact, bird populations are increasing there, while they are decreasing especially in agricultural landscapes, but also in forests. Blaming these declines on cats would be far too simplistic. The greatest threat to biodiversity is and remains the progressive degradation of habitats by humans.
https://www.nabu.de/tiere-und-pflanzen/voegel/gefaehrdungen/katzen/15537.html
They recommend castration to limit the cross-breeding of house cats with wild cats, but see no general problem in free-roaming house cats.
