The cross-play issue between Battlefield 2042 and Battlefield 6

I purchased Battlefield 2042 on the Epic Games Store and Battlefield 6 on Steam. The Steam version of Battlefield 6 does not rely on the EA App to launch, and I do not see my pre-ordered Battlefield 6 in my EA game library. Both my Epic account and Steam account are linked to the same EA account.

Therefore, I would like to ask: if I upgrade the free pass that is linked to Battlefield 6 through Battlefield 2042 on Epic, will the related skin rewards be properly delivered to my Battlefield 6 account on Steam where I pre-ordered the game?