Hey again guys, I think i've found the solution. After doing this Deathstorm Part 2 finally became playable for me, no more of this half black half white screen issue. You've just got to re-download and install the dlc.
If you don't know how to do this (because I sure didn't until I looked it up!), I'll go through the steps below:
Turn your PS4 on and find the Sniper Elite 4 game icon on the main screen. When you have the icon highlighted, press the down arrow button on your controller to bring up an options menu, this menu should include the PlayStation Store at the bottom. Press the down arrow until the PlayStation Store icon is highlighted and press X. That should bring up a menu where the first box is "Your Add-Ons". Press X again and you should get a list of all the add-ons that you have purchased or had the codes for. Use the up or down arrows on your controller to highlight Deathstorm Part 2: Infiltration. It doesn't say "download again" but that is what the two dots and an arrow mean. Just press X and the add-on should be downloaded again. Find it in your notifications from the main screen and after it's finished downloading it should say it's waiting to be installed. Install it, then wait for it to finish before turning off your PS4. (I don't know if turning it off is crucial but I did it just to be safe lol) Turn your PS4 on again, open Sniper Elite 4, go to your dlc missions and try playing Deathstorm Part 2. It should work.
This is how I did it, after looking up stuff online all day trying to fix it with little luck. I can't believe all this time it was so simple. Hopefully it works for you guys too if you're still having this problem.