I think it's a little unclear, although it seems that the character continues to exist in the present. I base this on the character's last appearance (which occurs after that which you cited) and what followed:
We last see past-Gamora as Quill encounters her near the finish, I think, of the big climactic battle, after she and present-Nebula have killed past-Nebula. (I've seen it once so I'm relying on imperfect memory here.) As he touches her cheek, past-Gamora kicks Quill in the nether regions (twice). Then she asks Nebula, "This one, really?" Nebula answers, "It was either him or a tree." This gives the impression that Nebula has, off screen, already told Gamora about her relationship with Quill. Having now met Quill, past-Gamora is not impressed. I also had the impression that past-Gamora survived the battle, although we don't see this on-screen. The moment where we see Quill searching for her, immediately before bantering with Thor, suggests to me that past-Gamora has stayed in the present but slipped away rather than joining the Guardians. However, that's merely an interpretation. I do agree it potentially sets up "Guardians of the Galaxy 3: The Search for Gamora."
One of the deleted scenes to be included on the DVD of Endgame was released on July 26, 2019. It reveals that Gamora survived Tony's snap and shows her turning and possibly walking away from the battlefield. Source: USA Today article with scene.