There really isn't a way to rank anyone with puzzles. You either you solve them or you don't. You might get away with an event solving as many puzzles correctly in a limited period of time. However I feel that would be more of a personal training thing.
What about 1 vs 1 games in tournament? Who solves 3 puzzle faster that is winner. If someone berserks he must solve more puzzles Chess.com has puzzle rush and lichess must answer it
Maybe this can serve as inspiration. Although I somehow feel like having such a competition online might be particularly susceptible to engine cheating.
I forgot one important rule - if someone makes mistake he immediately loses game so it will be difficult to have long winnig streak, witch is good i think
The community (which is this thread) will shortlist interesting chess puzzle. Then they will be arranged by their ratings. There will be various checkpoints (like 1600's puzzle, 1700's puzzle etc). Losing would force the player to restart from the previous checkpoints. The one to reach the highest level in a given time would be the winner.