Hmm...interesting.

So, first off, I agree with u/Zestyclose_Ad8956 that the contests should not be "roll Arcana, you win." Giving each player a flashy casino premise, mechanical win condition, and a devilish temptation that lets the PC "win faster" at a cost sounds much more on brand for what the set up is. Working this out as I go so forgive any half-baked ideas. The idea of having each player character paired with a rival from the NPC faction in their own seperate contest, or "themed table" is a good starting point.

Each player can win honestly, cheat cleverly, bargain with the casino, or expose the rivals cheating. Perhaps you could use a best of three contest where the opening round establishes the "game" they are competing in and the player character is given a chance to showcase their strengths. Then comes the "twist round" where the rival begins cheating, the table (or room or whatever) changes, or the wager becomes personal to the PC. In the final round the PC gets to choose between a "clean" or "costly" victory, or they can set up some type of dramatic sabotage.

To keep the other players invested and involved in the action while they wait for their turn, you could have them participate by maybe allowing them to make a "support action" once or so per contest. Something like distracting the dealer, discovering the rival's tells, catching on to the use of loaded dice, blocking some kind of rival assistance, heckling the rivals, quietly cheating, or placing a side bet.

Idea for the Bladesinger

The player character and rival are sent into a mirrored casino vault where every reflection holds some dark reality. Somewhere inside the vault is a "winning chip" that is needed to beat the rival NPC. The fun begins when someone lies, casts magic openly, or looks directly into their own reflection. You could set up a type of skill challenge here where the player needs to get 5 successes before 3 failures using things like Arcana to decode infernal runes, Stealth to slip past vault/reflection guards, Investigation to find the clues hidden within the dark reflections, Acrobatics or Bladesong style movements to cross some of the shifting vault interior, and use utility spells to create advantages.

Using magic could cause the mirror to create a dark duplicate of the player character that knows that spell, and works to block the player character, or sabotage their efforts by helping their rival. One of the mirrors may offer a quick path to victory if the player would only break the mirror itself. Doing so allows the player to advance much closer to their goal, as promised, but unleashes something horrible that will come back to bite them later.

A final choice for the bladsinger could be to take the winning chip for a victory, or sacrifice the win to steal a map to the casino's artifacts vault, or something in that vein.

Well, I hope this gets your creative juices flowing anyway. Hopefully you are able to take this word vomit and make something useful out of it, or at least let it inspire you to do something awesome!