It does, however, look like there's still always a lighthouse.
The yet-to-be-named BioShock 4 is currently under development at Cloud Chamber, a studio with multiple locations established by publisher 2K specifically to work on the series. It would be too far of a stretch to call it the successor to Irrational, the Seattle studio led by Ken Levine that developed Bioshock and Bioshock Infinite, but Cloud Chamber does boast plenty of series veterans that have been involved from the start, including the game's design director Jonathan Pelling and a creative director with the best name in the industry: Hoagy de la Plante.
Cloud Chamber has now posted several dozen new job openings (first spotted by VGC) and says it "is currently recruiting like mad for game developers in two amazing locations" in San Francisco and Montreal. The 29 roles range across production, design and other skillsets, though notable by its absence is any mention of multiplayer (Bioshock 2 had a half-decent multiplayer mode, while Infinite was conceived of as a multiplayer title before abandoning the idea mid-development). There's not much known about Bioshock 4, but one of the sure bets is that it's a singleplayer shooter.
The studio's description of the "next BioShock" is fairly boilerplate, all about the "thrill and responsibility of creating the next iteration of such a beloved game", though the combat designer job description has a few more nuggets about what Cloud Chamber's going for. Descriptions like "immersive sandbox world" are pretty much what you'd expect, but the listing does get more expansive in seeking designers who can "get creative: look beyond direct conflict, accommodate various play-styles and design encounters that can be resolved through player ingenuity."
Sounds great, though I have to admit I basically waltzed through the first Bioshock zapping everything with electricity then shotgunning faces. Hey, it worked great!
Bioshock 4 was officially announced by 2K way back in December 2019, since when the publisher has kept schtum about the project. The only details so far have come courtesy of leaks, notably Youtuber Colin Moriarty claiming that "It takes place in a 1960s Antarctic city called Borealis. [The game's] codenamed 'Parkside'… I’ve been told that the development team has incredible latitude to get it right."
An arctic research station is certainly the right kind of vibe for Bioshock, though the above should definitely be taken with a whole shaker full of salt. One element that does ring true is the "latitude" 2K is granting Cloud Chamber: at this point it's been over a decade since 2013's Bioshock Infinite, and 2K clearly sees this series as having the potential to be around for a long time if it can get this one right. Infinite itself sold well enough, but isn't looked back on with the same fondness as Bioshock or Bioshock 2, so Bioshock 4 needs to not only build on that legacy but re-introduce the series to a whole new generation of players.
One obvious factor that should probably be mentioned: Ken Levine, creative director of BioShock and Infinite, isn't involved. After Irrational's closure, Levine set up Ghost Story Games with 2K, which is currently working on the very Bioshock-y looking Judas instead.
If you spend long enough on Cloud Chamber's website you might start to think you're seeing clues. There are the logos of the three previous entries, followed by a placeholder logo saying "Next" where you can just about make out some murky outlines. There are pipes belching steam clouds. And right in the middle, staring you in the face, is a simple and elegant illustration that calls to mind Infinite's parting shot: "There is always a lighthouse, there's always a man, there's always a city."
