How to share DLCs between different accounts

Let me approach the answer from a different angle.

Each PS4 can have up to 16 accounts at any given time. One of them can be on auto-login, otherwise you have to select one for the controller you hold. Every owner probably knows this. Those accounts can either be purely local, potentially be linked with a PSN account in the future, or already be linked with a PSN account. (The PSN-part of those accounts can be logged out, but never unlinked again.) Deleting an account on the console deletes only the local part of it, the PSN account stays untouched.

Every of those accounts can be made “primary” on one PS4. Note that several/all accounts can be primary on the same console! Also note that one PSN account can be represented on several consoles as well.

A PSN account can only be logged in on one console. As soon as it is logged in on another one, it is logged out on any other console. The account still stays on all console (just not logged in).

Now it comes: the downloaded content a PSN account has associated (i.e. bought (for money or “free”)), can be used by that very PSN account wherever it is logged in (online) and by every account on the console where that account is primary on (console can even be offline).

The PS+ online multiplayer “right” is also shared. PS+ savegame upload or the right to add the monthly games to your library is not shared. But the right to play downloaded monthly games is shared like any other game.

Now the tricky part: not everything in the PSN store is “downloadable” and those things are not shared. And the nasty part is: that does not just apply to in-game credit bundles, some “DLCs” also fall in that category unfortunately (e.g. Division 2, see examples below). And there is no way to distinguish that before buying! (Most DLCs are (tiny) downloads, though.)

DLCs bought directly through the installed game page are compatible cross-region. If incompatible, you would not see the item, or it would be marked “unavailable” for accounts from incompatible regions. – The in-game shortcut to the PSN-store will often not work cross-region, though.

Additionally: I do know for sure that some games have different versions in different regions (which can be installed alongside, like 2 different games!). Those do not share savegames. (This can especially be seen if the in-game language choices change between regions/markets.)

I believe if you go directly to an add-on/DLC through the game page of the installed game you will either get a compatible DLC or it will not be listed in the first place.

Examples:

• Overcooked 2
  • all DLCs are part of the base game download (but locked)
  • the DLC downloads (1.1MB each) are like unlock keys
  • all is shared the usual way
  • two accounts can play it simultaneously
    • they can even join up online (2 players play 1 copy)
  • you can also do share play (2 players play 1 copy)
    • share play does not support several players on the remote console
  • you can not combine share play with online play
    • i.e. you can’t have 3 players with 3 PS4 consoles playing 1 copy of the game
  • You can have up to 4 players (game has max. 4 players) on 2 consoles (or 1 console: only couch multiplayer)
• Overcooked All You Can Eat edition
  • the game does not allow share play any more
• Watch Dogs
  • some (all?) cosmetic DLCs are unlock keys only (1.1MB)
  • the big story expansion is a big download
  • all those are shared
• Watch Dogs Legion – Ultimate edition
  • the big story expansion is a unlock key only (1.1MB)
  • the Season Pass is a download as well (key)
  • Ultimate Edition Set is also a download (key)
  • at least one benefit of the Ultimate Edition (4 weeks VIP) is only for the account who bought it
  • the downloadable parts are shared
  • this game is one of the few examples where:
    • the game (and the included DLCs) is on a Brazilian account
    • viewing the game page on a German account I do not have the possibility to buy the game or any DLC for it
    • on other cross-region cases I get the offer to (double) buy game and DLCs
• The Division 2 – New York Edition
  • the base game includes all data
  • but the big (story) expansion has no downloadable unlock key
    • it is only shown as “bought” in the library, but no download
    • not shared; only the buyer can play it (which adds a lot)

The "Primary PS4" you refer to only works for games.
DLC are region locked. In your case, the DLC you bought is only valid for your German account, and you need to be logged on the PSN with that account in order to use it. You can try calling the Sony customer service and explain them the situation, maybe they can switch the DLC to your other account, but I'm pessimistic about it (I haven't found their customer service very helpful so far ...)

I think you could have used the German code in your Italian account.