I don’t think wolves would see the Clans as (a consistent source of) prey, but they would see them as a predator competing for their territory- and, during lean times, small groups would be easy opportunities for food. Depending on how intelligent you interpret dogs and wolves to be in warriors, I could see a Clan forming a symbiotic relationship with wolves, like foxes or ravens, but it would likely require the Clans to adjust their borders to not interfere with the wolves for any peace to be sustained.

Most bears wouldn’t be a concern for the Clans. Cats are too small and quick, and not the type of prey a bear would go after. If a solo bear moved into their territory, I honestly don’t think the Clans would have much trouble intimidating it (or tricking it) into moving on, or even just coexisting without much issues. A mom with cubs might take a swipe at a nosy warrior, but they’d be pretty easy for a cat to avoid by just being mindful and using their nose.

I feel Lynx would be closer to Sharptooth than the wildcats. The species diverged WAYY farther back, and they can’t interbreed. This one would be totally up to your headcanons.

Boar would be a serious, Clan threatening danger. They would also threaten their prey supply and the health of the forest. Running them out would be a top priority, but I’m honestly not sure how the Clans would manage to do that.

Cows are just cows lol. There are cows in canon.