Game licences are controlled by the platform you bought it on not by Bungie.
With games pass you are given access to the licences but do not own them (rent might be a better term).
So if you bought a dlc licence from Sony you that licence is only for the PlayStation so you can not access it on a XB or PC.
Until you buy a licence to that other platform the provider to that platform will not allow you to play.
This is due to each platform getting a percentage (on average around 30%) of the purchase price.
In the case of the XB and PlayStation they make next to nothing from console sales with most of their money coming from their percentage of game, dlc and in game currency sales.
So they want their share of the money before letting you have any licence to their platform.
So if you own the dlc on PlayStation and want it for your XB then you have to buy it again for the new platform.