Cross Save PS5/PC Cosmetics/Hideout

Unfortunately i can't find an explicit answer to my question. I know that i have to buy a Key on both Platforms PC/PS5, i already have the game on the PS.
My question now is, if i buy the $160 pack on the PoE Website, for example, will the cosmetics and hideout be transferred to my Account on the PS5?
Or, if i buy the pack on Steam, will I also have the Cosmetics and Hideout when i switch back to PS? My Account is already linked to both Platforms