I think you should post this in the Skyrim Special Edition forums because if you post it there people would be able to help you better with it as people on the Skyrim Special Edition forums would be familar with the game.
Here is link to it.
https://psteamcommunity.yuanyoumao.com/app/489830/discussions/

If you have obtained the Anniversary Edition, it can be a bit difficult to see if you actually have it.

What you could check:

Run Skyrim Special Edition.
Go to System > Settings > Gameplay.
If you can see "Survival Mode" listed in the gameplay settings, it likely means you have it.



Or perhaps you are logged in under the wrong account? And that's why you don't see any games.