Only local content saved to YOUR PS4 is deleted. Since this is an MMO, most of the relevant stuff is on the Neverwinter server. The only thing that goes away as far as I can tell is your graphics settings and a Terms agreement.
I figured out a fix a few days ago that has worked for me every time. From the home PS4 screen: Settings > Application Saved Data Management > Saved Data in System Storage > Delete > Neverwinter Delete the 10.49MB Neverwinter Saved Data. Once you log back in to the game you have to reset your UI and agree to terms of…