Sony says it’s up to those doing the upgrades as to what they want to do.
This upcoming generation of consoles is a different beast from the ending generation. For one, these systems are much more up to date with current technology than the PS4 or Xbox One were, but maybe more importantly, they’re backwards compatibility with the previous generation (and beyond in the case of the Xbox), which the PS4 and One lacked. Sony actually detailed their policy and abilities on BC recently, though there is one key thing of note.
As always, with a new generation of systems comes a lot of cross-gen titles, and some publishers have been handling it pretty smoothly with straightforward upgrades from current gen to next gen, while others…haven’t. But for those that do, it seems as if there has been issues on the PlayStation side with save transfers. Unlike Microsoft, who has their universal Smart Delivery method publishers and developers can employ (though some developers have opted out of using that system), it seems as if Sony is leaving it up to the developers entirely as explained on the official PlayStation blog.
“Please note that the ability to transfer game saves between a PS4 version and a PS5 version of the same game is a developer decision, and will vary title by title for cross-generational games.”
This explains why several titles that had PS4 to PS5 upgrade titles have lacked save transfers, such as mostly recently Yakuza: Like a Dragon and Maneater. Sony themselves, at least, seem to be doing it with the most recent announcement that Marvel’s Spider-Man: Miles Morales will have save transfers.