Clarification on Cross-Platform MTX

So, as I understand it, most MTX in-game are separate and unshareable between PC and PS5 (it seems the distinction is whether it's purchased? Like, league rewards earned in-game seem to be available on either side). I've made my peace with the fuss, and I've got a ticket in to move some stash tabs and maybe some Twitch drops from my old PS4 subaccount to the "right" one, all this is fine with me. My question specifically pertains to the Kirac Pass.

I currently own this pass on PC for POE1, and have earned all the rewards. I have the armour set assigned as my appearance, so it shows up on PC, but then on PS5, it'll show on the character select, but not in-game (currently using it in POE2, if it matters). My question is, if I wanted it to be functional in-game on PS5 as well, do I need to both purchase the Kirac Pass on Playstation AND complete all the objectives on PS5 POE1, since my atlas completion was done over on PC? This is a project I'm willing to undertake, especially if my stash tabs get moved sooner rather than later to the right subaccount, I just want to know what I'm expecting going in, as finishing the campaign and doing all the atlas bonus objectives are two significantly different goals to be shooting for.

Thanks for the help!