I can't open Moxxi's heist - ps4 - borderlands 3

I bought moxxi’s heist add on online, but I can’t open it. Seems like I haven’t bought it at all

Moved you in to the BL3 PS4 tech support section.

There’s a couple of potential issues: one is if your base game and the DLC were purchased for different regions (N. America, Asia/Pacific, etc.). If that’s the case, you’ll need to contact the store.

Your issue looks more like the one in this thread:

So, if you quit the game, go to the store, and check under “Purchased” (1) is the DLC showing and (2) will it let you install from there?

Is there any way to transfer the data from the European version to the US version? Or would I have to start from scratch?

I would assume save data could be transferred, as long as its to the same account (nothing in the terms against moving to a different country) - but the actual game + dlc would have a region specific licence; this you would have to contact ps store (support) for.