Can't say for sure obviously but I would expect so since you'll still be using the same online account and user name. I know when going from BF4 on PS3 to PS4 you kept your progression. Also BF1&5 on PS4 to PS5 you keep your progress, difference with those though is that it's actually the same game not a specific PS5 version.
I think they have even discussed cross platform progression as well I definitely remember reading that somewhere. That's always been an annoyance of mine as I play on PlayStation and on PC, having to unlock everything twice is a pain.
