Hazel has done very extensive research into this specific type of game experience. These are most of the titles shown off or briefly mentioned in her video on cosy anime RPGs (https://youtu.be/8xYhv15qv4A), although I cannot personally guarantee that they are all anime RPGs. These are just most of the titles I heard her mention :- )

Another user has also made a list for this video with all the main games discussed:
https://www.backloggd.com/u/CModel/list/hazel---cozy-anime-rpgs/