A Deathloop PS4 edition is being listed on the PlayStation Store, but that doesn't mean you can actually play it on that console.
As spotted on Twitter by PlayStation Lifestyle editor-in-chief Chandler Wood, the PlayStation Store listing for Deathloop Deluxe Edition is currently tagged for both PS5 and PS4, while the Standard Edition has the correct listing of PS5 only. This appears to not be an example of Sony locking cross-gen upgrades behind special editions (as it recently decided not to do with Horizon Forbidden West) but instead a simple mix-up with the store listing, especially since one of the bullet points of the Deluxe Edition's actual description is still "Designed for the PS5".
It's possible that a Deathloop PS4 version will arrive sometime after launch, though it would run counter to Sony positioning Arkane's latest as one of the system's biggest third-party exclusives. Console exclusives, that is, since Deathloop is also coming to PC.
More likely than Deathloop PS4 happening sometime after launch is a Deathloop Xbox Series X version dropping roughly a year from now. Developer Arkane Studios was part of Microsoft's big Bethesda buyout, which makes Deathloop prime porting material once its presumably time-limited exclusivity agreement with Sony expires.
In the meantime, the voice actor of Deathloop's protagonist is looking to score a PS5 so he can play the game on his own time; at least you know you're in good company if you're still trying to find a PS5 re-stock.
A Deathloop Easter egg hints that it may take place in the same fictional universe as Dishonored - give or take a few decades of cultural and technological development.