yesterday i completed the final step of the quest, i.e. IP playlist but at the end the vendor didn't offered any exotic to claim. I did all the encounter in order and without leaving at any point. Now the quest is complete and gone but i got no exotic claim token.
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IIRC the item is stored as a currency item (like mementos) rather than an inventory item (like spoils) and shows up on the vendor. Do you have a clip showing you interacting with the vendor after the run was completed and the Exotics not being listed?