The Bowser Jr. Team's Koopa Clown Cars represent the Toy-Con Car from the Toy-Con Vehicle Kit game.
The stage and music track represent the main island setting of the Toy-Con Vehicle Kit, which features a playable off-road vehicle.
The stamina battle condition references the Toy-Con Car's limited fuel meter, which will result in a game over when the fuel meter is depleted.
The Bowser Jr. Team's favored Clown Kart Dash and second battle condition reference the acceleration gameplay mechanic of the Toy-Con Vehicle Kit game.
Other trivia:
This spirit's Dash Attack ↑ ability further references the acceleration gameplay mechanic of the Toy-Con Vehicle Kit gamw.