This is pretty much standard behaviour for all PS5 versions, they are separate SKUs with their own trophy lists. It is also desired behaviour for a lot of PS5 owners (although some may prefer previously earned ones to auto pop again) as many value being able to play again for a new set of trophies.
So i did the update for the ps5 edition of Skyrim special edition. Started game and was asked to spend $20 for anniversary updates. Paid the Bethesda Tax. Downloaded the expensive mods. Played for 30 min and found a goblin and a backpack that increases weight limit. So far i like it. Oh, the load times are like 1 sec now on ps5 version. Very nice.
Finally got a game breaking bug. Not a single one of my saves will load. The game boots, the loading is normal, black screen... Music playing. But that is it. Tried resetting my ps5, tried different saves, all the same thing.