@___Smozoltov___ I was also in contact with EA Support who told me to uninstall the game, restore licenses on the PS4 https://manuals.playstation.net/document/en/ps4/settings/license.html and try to download and install again. I am not about to uninstall everything and redownloading right now, since my PS4 is on a metered internet connectionI and that would take up too much of my total download.
However, I have come to the conclusion that BF4 Premium is just not free for PS4 EA Access members. If you look closely at this page:
https://www.ea.com/ea-access/landing-page/battlefield-4
...it specifically states 'Xbox One' multiple times on the page. It's not very clear and should be communicated better by EA but that's the way it is.
Also, if you look at the bottom of this page, under Vault Add-Ons, it specifically states BF4 Premium with a Xbox logo.
https://www.ea.com/ea-access/games
It sucks, I know, since I specifically signed up for 12 months of EA Access on the PS4 because I was under the impression that BF4 Premium was part of the package. Now I'm seriously considering getting Premium for the PS4 (at 10% discount because of the EA Access membership) but I honestly feel misled and cheated...