D4 Ultimate edition on two platforms clarity

I preordered the ultimate edition of D4 for PC and also want to preorder for PS5. I will be using the same Battle.net account on both platforms. Do I need to buy the Ultimate edition on PS5 to get all the bonus cosmetics or is the standard edition enough and all the bonuses will be linked with the pc purchase?

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Iā€™m waiting for the answer too.