Which account / platform was the purchase made on? Your Xbox account?
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No the PlayStation 5 I never bought any of the dlc on Xbox
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What platform are you trying to play on? It looks like you set up cross save but you have selected your Xbox account as the primary account.
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playstion
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Are you trying to play on the same account you used to purchase it? If you are you may want to try restoring your licenses. https://help.bungie.net/hc/en-us/articles/360049196071