A prerequisite for there to even be a chance of cats being involved in ecosystem balance would be for the cats to exist purely as part of the ecosystem, as in being exposed to negative feedback effects to it (e.g. starvation due to overhunting). As it stands, they are being fed by humans and mostly exist outside the ecosystem, and every kill by them only drains resources from the ecosystem.

I think the majority of pet cats live in cities and suburan settings, which are anyway highly artificial ecosystems. Also, as noted in another comment already, birds are fed in the same areas also, and provided nesting boxes, which probably increases numbers (or rather the carrying capacity) quite a bit. Studies seem to show that diversity has gone down, but biomass has even gone up a bit over 50 years [1]. The loss of species is apparently also related to removal of old buildings and modern ones lacking spaces to breed for birds like sparrows and swifts, and removal of landscape features that specialists depend on. Maybe cats play a role though.

The linked article says 90% of the mortality is caused by un-owned cats. I'd imagine that feral cats just replace wild cats in Europe, and thus do exist in the ecosystem with negative feedback (if they are not fed). Not sure about North America, as there is not really a small wild cat species I think?

1 https://www.tandfonline.com/doi/full/10.1080/00063657.2021.1...

On the other hand, humans have done a pretty good job of removing most of the other predators in the environment. Domestic cats must be replacing some of the natural predation that is no longer occurring.

Not saying you are wrong, but we also feed birds and rodents, intentionally and by the by products of our society existing.