Yes it does. Your save file on ps4 Carrie's over as well.
At the moment, the ps5 version is identical and has no inherent advantages. At some point next season, possibly the start, the next gen versions will receive an update that allows for 60fps and some other graphical/performance enhancements. The input delay of the ps5 controller is the same as ps4 though, wo those changes won't offer any meaningful advantages over those still playing on ps4.
The same is true for xbone to Xbox S/X, except that the new system and controller has lower input delay than xbone. More comparable to PS.
"It may not be thick, but boy is it short."