Did I Steal Someone’s Pet?

I found a cat outside, he was sick and dirty, and later found fleas. no chip, no one in my area owned him, and no one was posting about him. Vet said the cat looked like a stray, that it’s a bit underweight, has a respiratory issue, and herpes. I got him a rabies vax and held off on other vaccines/neuter until enough times passed.

someone replied to a found post I made with pictures of the cat, as we talked they admitted it’s an outside cat they started feeding when he came around, they didn’t know when he went missing, and never made any lost pet posts, because going missing is normal for this cat. online humane societies recommend you request some kind of paper work, because it could be someone else’s outside pet, and people like to harm cats. i ask for paper work like vet bills, invoices, records, adoption sale or anything like that. they say the animal was never brought to the vet, and they decided to adopt him like the day he went missing. They think it isn’t fair to request papers on a stray because strays don’t have any paper work. We agree that I can keep looking at other claims for a few days before moving forward.

I ask the humane society for advice and they tell me it doesn’t sound like they own the cat and that it’s a community cat. I can give it back if I want but due to its condition they recommend that I don’t.

The other person changed their mind on waiting for other claims and started sending me emotionally charged texted messages, and made a public post that ended up doxxing me. Comments called to harass me, stalk me, and commit violent acts against me. A police report was allegedly made against me, but I called in and the cops say they don’t have anything like that. I don’t even feel comfortable meeting up with this individual anymore.

At that point I go in person to animal control (they weren’t answering my calls for a week), and explain the situation with all the info I have. They tell me that Humane was correct. They don’t own that cat, and in fact since I have been housing, feeding, watering, getting vet care, and searching for owners (no one has been able to claim and no missing reports on the animal) that technically the cat is mine.

Location: Oklahoma

EDIT: I do appreciate support here, but I came here to hear people versed in law around this, and I feel as if many people are just making guesses, or commenting what they feel is correct based on personal belief.

At this point I guess I just have to trust animal control because their job is to uphold animal related laws