The neighborhood cat I feed. She's so sweet.

Keep working on it until you can coax her into either stepping inside or into an easily enclosable space, then to vet for a chip scan.

Best case scenario is that she belongs to someone who misses their baby girl.

Second best case is no chip or previous owner super-sucks and therefore - you get a new buddy.

We invited an abandoned gray girl in for wet food one day and she never left. Starting on her first night, she’d wake me up in the wee hours giving me tiny kisses on my eyelids, cheeks, forehead, or tip of my nose. We still have her 12 years later and she is the sweetest cat ever. Don’t fuck with her though - she will cut you 🤣