Although it wasn't entirely intelligent of the guy to have created a thread for the pet found on PG, looking for an owner, but one's gotta appreciate his/her kind gesture. As far as the breed of the cat goes, I don't really think it matters much at this point but it would be very nice of the founder to post a picture or two so that anyone claiming the cat can be entirely sure it's his/hers.
If you put up flyers or post an adoption ad on olx or look for the owner yourself, there are chances that you will receive false claims and the cat would go in the wrong hands. Afterall, who doesn't fancy a free pet? Anyone claiming it could 'adopt' it and sell it for a handsome amount considering the cat is so playful and you said it's probably a persian as well.
I'd suggest that you keep it yourself if you like it and your family agrees to make room for it, spare time for it and be willing to put up with its tantrums. Otherwise, by all means contact a renowned PET welfare society in your area as alamode rightly suggested. The cat is better of staying in custody of the welfare rather than finding a scrooge who'd claim her and then treat her like a toy.
I hope the cat finds a good home and I do appreciate your efforts and intentions to put it where it belongs.
Best of luck.