Hi there!
DLC is licensed by the platform, not by Bungie. When you purchase a DLC, you are purchasing a license to access that DLC on that platform. This is how DLC has worked for years and is not an issue exclusive to Destiny 2 or Bungie.
DLC does not transfer between platforms, nor does it grant entitlements to DLC purchased on other platforms. If you wish to access the DLC on that platform, you will need to purchase it. Season passes or dungeon keys are purchased in game and can transfer with Cross Save, as they are redeemed immediately on the character set that purchased it.
For more information, please review the Cross Save Guide, linked below.
https://help.bungie.net/hc/en-us/articles/360049498031-Destiny-2-Cross-Save-Guide
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I am switching between the two platforms to play
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As noted above, DLC is licensed by the platform and not by Bungie. If you are moving to another platform, you will need to purchase the DLC on that platform.
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My epic platform has the DLC of the equipment I want, but I can't brush it out in Vex activities
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So when I perform vex activities, what happens when I don't give priority to dropping unlocked exotic equipment