During a recent and extremely long livestream in support of Final Fantasy 14, producer Naoki Yoshida gave away a little bit of info about the other game he's producing at the moment: Final Fantasy 16. Mostly, what he said was not to expect to see it at Tokyo Game Show this September/October.
However, development is apparently coming along at a decent pace. According to translation courtesy of Twitch streamer Aita Kimochi, the scenarios have all been completely written, and recording for the English voice-acting is close to being done. What's likely to keep it away from Tokyo Game Show this year is perfectionism, and a desire not to give much away before Final Fantasy 16 is ready for release.
According to Kimochi, Yoshida mentioned the battle system and "things that have not even been touched upon yet" would be in the next announcement, but that announcement won't be ready until shortly before release.
We're hoping that Final Fantasy 16 will come to PC shortly after a brief exclusivity window on PlayStation 5, but Sony remains tight-lipped on that subject.