She brings up her single status without prompting

It's never accidental. The casual, unprompted mention — 'oh, I haven't been seeing anyone seriously lately' delivered into a conversation that didn't ask for it — is a soft door being opened. She's not necessarily declaring interest; she's removing an obstacle. She's making sure you know the door isn't locked before she finds out whether you'd walk through it. The framing matters less than the unprompted nature of it. Whether it comes as a sigh about dating being difficult or a breezy reference to being on her own, the function is the same: she wants you to know she's available, just in case that information is relevant to you. It's a low-risk test — if you respond with interest, she knows. If you don't react, she hasn't committed to anything. The soft door opened into the room where the real conversation could happen, if you decide to walk in.