Oh so the publisher – 23 times – scene was not how they first met? Was that explained to the audience because I just watched it and I could only see glimpses of their past? Or did I miss it?

No, I think that’s how she tracked her down after, but the first time they met was what we saw that first flashback, at the concert. The 23 times would have been after they already had broken up and it wasn’t referenced at any other time, no. The timeline would have been:

Meeting at the concert -> other little flashbacks like in the car, by the lake, on the bed, and so on -> breaking up -> the 23 times search -> Vera sending Frank to Alice -> Vera going to Frank and Alice -> decades of happiness -> Vera finally telling Alice she looked for her in 23 different shops