The Forsaken Campaign, Tangled Shore, Presage, etc... has been vaulted. I'm asking a similar question myself as I've enabled cross play / cross save - and wondering if I need to buy the Forsaken DLC.
I suspect getting the Forsaken DLC is not needed as you can't actually access the content at all. Waiting to hear back myself - let's hope Bungie have an answer for the both of us.
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the forsaken campaign along with the tangled shore has been vaulted. the foresaken pack gets you access to the foresaken weapons in the lost light kiosk and access to foresaken end game content, i.e. the raid, dungeon, etc...