The game has been developed since 2019 by Cloud Chamber studio.
A supposed image of the upcoming BioShock game, which we will call BioShock 4, has recently been leaked online. The image was posted by the page MP1ST (via IGN), who said he discovered it in a film by a visual effects artist working for distributor 2K.
According to the site, the image is taken from an early version of the game, so it's likely already old and doesn't reflect what the new BioShock game will look like when it's released.
BioShock 4, which still has no official title, was announced in 2019 by 2K and is being developed by Cloud Chamber, a studio that includes some of the professionals who worked on the original BioShock. Little is known about the project, other than that it will be set in “A wonderful new world”That means we won't be returning to Rapture or Columbia, where BioShock 1, 2, and Infinite took place, respectively.
BioShock creator Ken Levine was not involved in the game. After leaving Irrational Games and closing the studio, he founded developer Campfire Games, which was renamed Ghost Story Games, and has been working on his new game Judas, which has yet to have a release date.