We've not heard anything official about the next Bioshock game in years, and from the looks of it, this may be because it's stuck in some sort of development hell.
This rumour comes from Oops Leaks over on Twitter, who said that the project has been rebooted four times since work on it began, and that the fourth reboot came in the summer of 2022. Oops Leaks believes that some things are staying the same despite the huge changes, like the setting, but with the constant changes in development teams and gameplay concepts, we're likely looking at a bit of a mess right now.
The last time we got a new Bioshock game was over ten years ago, when in March 2013 we saw the release of Bioshock: Infinite. We've had DLCs since then, but no new game has been launched for a long, long time. Fans have hoped for something concrete with each passing year, but it seems unlikely now we'll be getting the next Bioshock game anytime soon.