it's about the ruins of Rapture being discovered in the modern day. Since Rapture was built in secret and very little know that it even exists, with fewer knowing anything substantial about it, you're here as basically an archeology to figure out what the hell is going on here.
By this point, Rapture is gone. The power went out years ago. The number of remaining air pockets can be counted, and the city is just a series of concrete and rust pillars like a sea of headstones. Most of the game would be spent in a small, heavily armed and armored submarine or in a diving suit.
But the city is not uninhabited. There are still Splicers, but now they take the form of degenerated chimeric hybrids of human and sea life, like fish, cephalopods, crustaceans, seals, and more, like the wackass mutants shown off in the concept art for 1 and 2, due to them all being more plasmid than man by this point. A few big daddies still amble about, although the little sisters are long gone by now.
As you explore the ruins of Rapture, you'd have to use the submarine's weapons alongside your own person kit to fend off Splicers and hostile sealife, like giant squid.
I imagine the mysterious Luminescent Biomass and the origin of ADAM would feature heavily.
