Possibly Stray- Underweight?

Hey all- hoping someone more knowledgeable than me about this of cat can chime in about the size of this female and if I should put food out for her. I am aware she is a fancy cat- not asking about that- but that does factor into my thinking she's probably got an owner.

She's been visiting me for a few months now inconsistently - once every other week or so - even through the winter. Today she showed up looking a little skinnier- and I am questioning if I should put out food for her. I don't want to step on her possible owner's toes- but I am only assuming she is owned because of her markings. No collar or anything identifying though.

She's also very well socialized- and I can pick her up and give her snuggles. Today she also asked for belly pets- she did the flop and meow- and enjoyed the pets.

I don't want to own this cat- not looking to thief somebody's baby- but I do want to make sure she's not going hungry. My house is at capacity for pets. I've got 1 cat of my own, 1 hospice foster cat, and 3 oversized very stupid dogs (2 of my own, one foster) that would want to snuggle her.

So- should I feed her outside? Do we think she's underfed? Do I send snail mail to the neighbors asking about ownership? Does she look like she requires vetting? Kitty has no collar, no immediately visible spay tattoo. I would prefer to avoid an unnecessary vet visit for what is likely a neighbor's cat if I am overthinking this.

Poster Age: adult in US, have access to vet care, female cat, unsure if spayed