Terminology – What is the ‘Cosplay RPG’ genre?

tl;dr: The game is called a "cosplay RPG" due to the class and skill system revolving around characters wearing "costumes" (e.g. The fighter costume, the archer costume, etc). The genre name itself is part of the way the Tales series games are all marketed.

The Wikipedia page for this game states the following:

The game's characteristic genre name is "Cosplay RPG".

This is apparently a term specific to the Tales series of games. The page linked in that quote includes an explanation of the idea of "characteristic genres":

In the Tales series of games, a characteristic genre is a genre label that, in addition to labeling the games as role-playing games, illustrates a particular plot theme or noteworthy aspect of the game.

The concept of a characteristic genre derives from the idea that each Tales game is a unique experience not shared by any other game in the role-playing game genre. To reflect this, the developers create a new type of "genre" where each game would belong, defining its main focus and theme as part of its genre. The Tales game placed within each genre becomes the sole representative of that genre category, placing emphasis on the individual value of each game independent of others in the same series.

Based on information in this guide, the reason this game is called a "cosplay RPG" is related to the fact that the class/skill system revolves around "costumes" worn by your party members.

The list on that page includes other characteristic genres like "For Your Sake RPG" and "Passion that Illuminates the World RPG", so it's pretty safe to say that these genres aren't actual genres you'd find a list of games they categorize. The characteristic genre is just a descriptor for the individual Tales games.