I would imagine it is open… we used it several times during the last few months. Most recently, about three weeks ago. Now and then it is randomly closed off for private events.
I would think you could just show them your AP and they try their best to accommodate. Typically though I make a reservation and add in the notes section ‘Navigator Club if available’.
It hasn't been very busy when I have been there, but I tend to eat at off hours. One trip I had a Confisco Grille reservation and just asked at the stand if I could eat upstairs. In May 2022 I didn't have a reservation at all, just walked in. There were only a few other tables occupied both times.