The PS4, like probably most consoles, saves all it's user data - including what are referred to internally as 'entitlements' - on their own server, linked to a PSN (or what they're trying to call 'SEN') account. Therefore, generally speaking, cosmetic and other DLC purchases don't follow you to a different console.
However, in the case of that wretched game, Fortnite, this isn't the case - cosmetics and other entitlements are saved on Epic's servers, so you don't lose anything no matter what platform you use.
Having never played ED on a console, I am assuming that you cannot log into say, the PC version of the game if you only play a PS4 version - the log in details are different?
And yet, our Commander data is server side since Elite Dangerous is an online only game - even in Solo. And the store purchases are done through FD's own with points, albeit bought through the PS store. Who knows.
I just hope we don't get suckered into rebuys all over again when the content is far from good value. 800 points per ship kit! Lol.