Is this your cat? (Eugene)

Hello friends and neighbors. I live in the area of Jefferson, Washington and Lorain Hwy. Close to where Loraine ends and comes out into 29th and Washington. We have recently had a neighborhood cat stopping by our back porch. She seems healthy, but she seems to be around quite a lot and acts hungry. We can’t tell if she (he, idrk) belongs to someone in the neighborhood and before I get super concerned about her well-being, I wanted to try to put the word out and see if she does indeed have a safe space to retreat to during these winter months. She head butts pretty hard against your hand and has been down to receive and accept pets. She’s brave yet cautious. I’ve attached pictures for reference. Edited to add all her paws are white except one front paw has a “toe” sticking out. And she has a little tan mustache.