All DLC is delivered as separate .nsp files roughly 10-50 MB each. They require the base v1.2.1 update to function; attempting to install Wave 5 DLC on v1.0.0 will result in a corruption error.
While there were no major official content expansions released specifically in 2021, on Nintendo Switch reached its definitive state following a series of free updates that added fan-favorite characters and technical refinements. Final Character Roster & DLC kill la kill the game if switch nsp dlc updat 2021