FIRST, For those who can't find the DLC content on the store, you should try just searching "Battlefront", and look for "Bespin", "Rogue One: Scarif", "Death Star", and "Outer Rim". I just searched for that, and clicking See All allows you to find all of these items on the store. If that doesn't work for whatever reason, just find the main battlefront page, and look for the separate DLC items listed under add-ons from that page. Hope that helps.
AS FOR MY SITUATION
I've already tried pretty much every step in this forum, and I'm still at "content not installed" for all 4 DLC packs. I have posts on page 4 and 5, but I'll summarize, since it's still not fixed, in hopes that someone will care enough to try to fix it, rather than do workarounds that don't work for everyone. (Not being rude, but the problem has been an issue since December, if you search for it, since the VR mission came out basically, so...)
Here is the timeline of what I've done. (buying stuff and problems)
-Bought SW Battlefront on sale on PS store. Played it a little bit.
-Bought SWBF Season Pass a few weeks later, also on sale, from PS store. Played each one to try out the maps. (someone pointed out "nobody had played the DLC before coming here, which is incorrect in my case. I played each DLC pack before the issue happened)
-Bought a PS4 Pro and switched everything over. I don't remember playing it after installing it before the next step.
-Reformatted old External HDD to work with my PS4 Pro shortly after the update that allowed HDD to work.
-Ever since (either JUST the Pro upgrade, or after HDD also) My DLC says Content not Installed.
Here is what I've tried since this problem. (only after Content not Installed)
-Restart SWBF, Restart PS4.
-Delete SWBF, Reinstall SWBF, Move to Internal HD, move to external HD.
-Click the little down arrow that you can find next to each DLC item, by highlighting SWBF on my dashboard, hitting down, selecting "PlayStation Store", "Add-ons", and highlighting the down arrow next to each item. This is the only thing that actually pushes the content thru to my PS4. Apparently this refreshes the Licenses for each item, as a 1.1 mb file. Still doesn't work. (by pushes content to my ps4, I mean, it says downloading X, then shortly after, X installed, where X is whichever DLC)
-Logging onto PS store from PC, and attempting to download each DLC separately. This makes the button say "downloading to PS4", then it says "Playable", and DOES NOT push the install to my ps4 for whatever reason.
-Logging onto PS Store from my phone via the PS app, and doing the same as previous step, same results as well.
-Attempting to download DLC individually from the PS4 PS Store.
-Accessing purchase history from the PS Store site and trying to redownload from there.
-Ensure that my PS4 Pro is my primary device. A few times.
-Restore licenses for my account. Several times.
-After trying to play single player a bit for trophies, I realized my save data wasn't transferred from my old PS4, so I deleted my save data on my Pro, uploaded PS4 data to the cloud, and redownloaded it to my Pro, and successfully retrieved my data on my Pro.
I really have no idea what to do anymore. I don't even really want to play the game at the moment, but if I did, I'm limited to what I can play, despite paying for the DLC and playing them in the past. And the amount of time I've spent just TRYING to get this to work, and typing all of this up, could have been spent doing something productive. Again, not trying to be rude, but it's incredibly frustrating at this point.