Heyo! You’ll have to purchase the DLC on each account you plan to use. When you purchase DLC, you are purchasing a license to use the software on that platform—it gets associated with your platform, not your Bungie account. Here’s what Bungie has written on the topic:
[quote]Do my previous game purchases transfer across platforms?
Destiny 2 expansions (ex: Forsaken, Shadowkeep) do not transfer between platforms with Cross Save. Destiny 2 Season Passes (ex: Season of the Undying) do move between platforms on the characters they were redeemed on.*
*Exception: Destiny 2: The Collection on Stadia includes Season Pass access at no additional charge. Players who have Cross Save enabled with their Stadia account who would like to access Seasonal content on other platforms (PlayStation, Xbox, and Steam) will need to purchase those Season Passes directly on one of those platforms. [/quote]
Hope this helps!