What Ultimate mode supports playoff brackets with up to 32 players? Tourney.
Tourney is the dedicated tournament mode in Super Smash Bros. Ultimate. It organizes entrants into a bracket, allowing matches to progress through successive rounds until a champion remains. The mode supports tournaments of up to 32 players, making it suitable for a large local group rather than only a standard one-on-one battle.
Ultimate contains several similarly named multiplayer options, which can make this question easy to misread. Squad Strike has players select teams of three or five fighters, but it is a battle format rather than a bracket tournament. Smashdown also changes character-selection rules: once a character is used, that character is unavailable for later rounds of the session.
Tourney is not the same thing as Nintendo's online ranked matchmaking or a real-world esports event. It is an in-game bracket tool. Players can still customize battle rules, such as time limits, stocks, items, and stage choices, depending on the tournament setup.