[Jotaku]

By best anime RPG games on PS4 you look for, we assume that you meant by single-player & role-playing anime games without needing to be a MMORPG or an anime game with a multiplayer feature. 

Following is a list of 5 best anime RPG games on PS4 based on Best Anime Games Ranked By Gamers database as of March 2021:

Persona 5

Tales of Berseria

Ys VIII: Lacrimosa of DANA

The Legend of Heroes: Trails of Cold Steel IV

Atelier Ryza 2: Lost Legends & the Secret Fairy

* All of them are confirmed to be "role-playing" (RPG) genre in Wikipedia pages of those games.
* If you want to check "Best Anime Games" of all time, but not restricted to RPG genre, check out Best Anime Games Ranked By Gamers database.