They made sure you knew they were single

Nobody mentions being single twice by accident. Relationship status comes up in conversation about as often as anybody's job does, which is to say, when a person wants it to.

How to read it

The signal is not the fact, it is the delivery. Being told once, because it fitted the conversation, is ordinary. Being told again, unprompted, when nothing led there, is a door being propped open deliberately.

It is also one of the few things here that costs the other person something. Saying it out loud is a small risk, and people take small risks in the direction of what they want.

When it means nothing

It means nothing if you asked, and less than nothing if it fell out of a story about somebody else. It also means nothing if they announce it to whole rooms — some people lead with it and always have.

Your move

You do not need a clever response. The right answer to a door being opened is to walk through it, which means suggesting something specific with a day attached to it.