Bear with me, but if we were to give character animals as symbolism, then Denji is clearly a dog. Pochita was a dog and the irony on how Makima found Denji and treated him like a dog is underlining this.
In reality the devils are not really portraying that animal, but rather the fear that comes from the devil. As mentioned earlier, I think Mkima mentioned it that the devil's strength is gauched by how fearful the object of representation is. Chainsaw's are a typical fear, because the human knows it is a tool of destruction. And naturally it elevates the chainsaw's powerlevel's high.
We now have alot of devils introduced that underline the chainsaw man powersystem. Ghosts, a spirit deity, guns, bats, eternity (being stuck) are natural fears of humans, to the unknown, to the otherworldy, to weapons...
A cat and mouse game? I don't see anything like that, but looking at this and Makima, we can maybe figure out what powers Makima owns.
Denji, or atleast his human self is already indicating her powers, and Himeno is giving us more clues:
Makima is a woman and Denji could indeed fear a woman, knowing how unripe and horny he is...Denji carries this kind of barrier with him. But is AKi the same? For Himeno it looks like Makima would keep Aki away from having a romance with Himeno which indeed leads to Himenoi and Denji teaming up for romantic goals. Is Denji now afraid of women and could Makima be some "Woman Devil"? No. Makima's powers are mostly reated to her eyes, is she contracted? Maybe, is she a devil herself? Maybe yes. What Makima does is using her womanly charms, and Hibari is not a target, no, it's the men, Aki and Denji two human's that contracted extraordinary devils. Using her womanly charms, Makima MANIPULATES both Denji and Aki and probably other men for her own ideals and goals. So my first guess is that Makima is a "Manipulation Devil", or contracted with such. Manipulation is something we all fear, especially people that live in a nation that is currently warfaring against another nation. Information war exists and having your reality and history being changed is something very uneasy to carry around. Makima uses this in order to change the reality of her targets and thus maybe manipulate their goals and how they move. Denji and Aki also are both perfect targets BECAUSE they symbolize animals, and dogs and foxes, but especially dogs are easy to educated, which is how Makima actually utilizes her manipulation against Denji. What are the real effects of the Manipulation from the Manipulation Devil? I think it allows Makima to look into her targets and figure out their weaknesses, in order to manipulate said target.
So Makima can't be the cat and knowing that those working in her squad are maybe symbolized as animals...it leaves only two interesting characters out, Power and Kobeni.
I don't think that Power symbolizes a cat tho, cats are actually clean animals that clean themselves. What is more important to Power's character: Her affection towards animals, and with that her affection towards the group.
This leaves our final option:
Kobeni is the Cat. I know this is absurd and may be a stretch but this is just a gut take from observation.
The Kobeni - Denji dogcat game has been teased in the Eternity Devil arc. Kobeni stabbed Denji, then later on regretted it. Mostly due to fear.
Fear is the main quality of Kobeni's character, she is easily feared, she is always frightened about little things. Going back to the powerlevel system I mentioned earlier...Kobeni is that sorta gagcharacter that tries to sense those powerlevels and then manifest them through her crazy reactions and loss of cool. What if we make Kobeni a character that functions in such a way, she can gauche said powerlevels and maybe even see throughout a scenario and see how bad it goes? Her life seems to go downhill anyway, she has always been aware of it, be it ending up as devil hunter, or...prostitute. Kobeni seems to be chased by bad luck and it has been underlined with the newest episode. But guess what? A cat has multiple lifes xD.
A cat in the end can't be a power, or can it? I am thinking about a common symbolism of cats and I want to look into mythology, something that's too common and fits in the griddy world of CSM: The Black Cat, aka the bringer of bad Omen.
Ever heard about the superstition: If you come across a Black Cat, your luck is about to be doomed?
Something even my parents teached me as a young kid...naturally...there are some people out in the world that believe in such superstitions. Religious people...old and wise people that lived all their life facing superstitions...it exists and it induces fear. Is there any better ability to give to a support character, than being the manifestion of this and being able to use her power in order to determine current danger levels and threat levels? I think this would be fun! Also this explains pretty much, why Kobeni doesn't want to reveal her contract, because she thinks if people know her being the cat devil, would possibly cause the others to fear her and leave her alone. Maybe she faced something similair in the past?
Atp I think there are also other doombringing animals, like The Black Crow that serves as Omen for something bad to happen. Kobeni could be also a Black Crow, but it would still be much more flavourful if she were the Black Cat.