I think that I watched the same rough machine-translated sub that @glilimith@lemmy.blahaj.zone watched, and I pretty much agree with their assessment:

The year is 2205, and various famous Japanese swords have been incarnated in cute male human form, to be sent back in time to fight shadows created by a similarly time traveling enemy who are trying to change Japanese history.

edit: A translation calls the enemy “historical revisionists” which makes the whole enterprise sound Japanese right-wing…

This latest show is an adaptation of Touken Ranbu 2.5D stage shows, which are adaptations of a card collecting browser and phone game by DMM, who also produce the popular Kantai Collection/KanColle franchise with girl incarnations of battleships.

Too many characters, knowledge of Japanese history and the prior shows introducing all these other characters.

edit: Maybe this is only for fans of the game.

Gameplay looks like this.