Yesterday I treated myself to skyrim v special edition with all addons in the PS store.
Now the 3 addons are in the menu under the tab "Downloadable content" in the game, but can't be selected. For me, downloadable means I don't have it yet, but I can get it. How do I get the addons?
They are integrated in the game. You don't have to download it separately.
Just like ghstx1337 already described below, the addons are already installed. In Skyrim, "Downloadable content" always shows the add-ons so you can see which ones you have.
It is possible that earlier in the so-called "Oldrim" version (a compound word consisting of Old and Skyrim, so old verse. From Skyrim before Skyrim SE) the content could be selected and downloaded there.
The add-ons are now installed automatically. Therefore, this view only serves as an overview and has no other function.
By "downloadable content" we mean any additional content that you already have, not what is downloadable. Your mods are also displayed there, should you install any. The Legendary Edition is already the full version with the DLCs, which are not available without them. That's why they are of course also installed at the same time.