The season passes (not battle passes) that are included in the deluxe edition give you the premium bonus stream. So yes, it is not necessary to buy something else.
That is just optional for ppl that want the premium bonus stream but don't want to buy the annual pass.
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Well, is there a version of Shadowkeep that comes with the battle passes so I can cancel my pre-order for the digital deluxe edition and buy that version instead?
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Sorry, I was not clear enough about that. There's no such thing as battle passes. There's season passes and they include the premium eververse stuff. You are all good, you have the premium stuff for 4 seasons in your deluxe edition.