I didn't purchase it with coins mine was through ultimate edtion on xbox however its only active on xbox and only gives free tiers on playstation from what ea rep said the pass doesnt transfer only store items like skins
It doesn't matter if you purchased it with Battlefield currency or with the Ultimate Edition. The Season 1 battle pass itself is purchasable with Battlefield Currency, which makes it an in-game purchase. And according to EA's blog about cross progression, it's supposed to be available on all platforms if you've purchased it once.
There's no way they would make Ultimate Edition owners buy the battle pass twice but let Standard Edition owners that bought the pass in game have it cross platform. They've made an error somewhere and need to fix it. No other cross progression game makes their players purchase their battle passes more than once.
