I'm chiming in here because I think this is wrong. Cross-save is a feature for a game that is designed for 2 platforms. So LBP3 on PS3/ PS4 or PS All Stars for PS3/ Vita.
In these situations, each platform has its own version of the game. DriveClub is not getting a PS5 'version': it's just the PS4 game being played on the PS5, so your save file will transfer as long as you have it.
Yakuza 7's situation is just straight up dumb. I wonder if MS paid for cross-save functionality because tons of other developers are not having cross-save issues (but I am not claiming they are, just seems strange to me)
Yakuza 7 on PS4/ PS5 are two different versions of the game. Yes, you can play Y7 PS4 on your PS5, but the PS5 update will make it more like a PS5 game. This requires the cross-save functionality for your save to transfer.
Dirt 5 is the same as well, another game with MS marketing.