[Jotaku]

There are 2 kinds of Japanese anime games on PS4 as of 2021 in this criteria.

1. Anime MMORPG developed by Japanese
2. Multiplayer Anime Games, which is developed by Japanese

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1. Anime MMORPG developed by Japanese

First of all, there are not many mmorpgs developed by Japanese for PC or major consoles like PS5. As you know, most Japanese anime games are buy-to-play. In fact, most anime mmorpg are actually developed by China, Taiwan, Korean and so on. So if you look for Japanese mmorpg then there are not many choices. Please note that, Final Fantasy XIV is not an anime game, but is a game with some anime characters. Thus when it comes to Japanese Anime Online Games and is serviced in NA/EU region, there are only following 3 anime games:

Phantasy Star Online 2 (PSO 2)
Onigiri
Caravan Stories

As of August 2021, Phantasy Star Online 2 is the most popular according to the Best Anime Games 2020-2021 Ranking database. This may change in the future.
Please also note that you can find much more Japanese anime mmorpg if you look for mobile games as well. But most of them are not released on NA/EU region, sadly.

However, there are upcoming anime mmorpg games called Blue Protocol, Project GAMM. They are all developed by Japanese and for major gaming platforms like PC, PS5 and so on.

2. Multiplayer Anime Games, which is developed by Japanese
There are so many Japanese anime games on PS4 when it comes to simple multiplayer.

According to the best anime games 2020-2021 ranking database, currently following Japanese anime games with multiplayer feature are the most popular as of August 2021:
Sword Art Online: Fatal Bullet
Kandagawa Jet Girls
Senran Kagura: Peach Beach Splash
Code Vein
Tokyo Ghoul:re Call to Exist

Please note that this may change in the future.