Absolutely love the art style, the dialogue of the characters, as well as the idea. Really felt like I was playing an old school RPG on my gba. Unfortunately as cool as everything about the game is, it did feel like I had no control over anything happening in the game, due to the nature of the rock paper scissors.
To increase player agency and not feel like everything is 100% random, you could maybe give the player the option to build their own deck. Alternatively you could provide the player knowledge on whats coming, so they can prepare for it, possibly in the form of being able to use a power to see what the next 3 cards your opponent will play, or even just straight up knowing what your opponent is about to play and then buff the enemy HPs and their power cards to increase challenge.
I don't know if any of this is a good solution, but some form of design decision to limit randomness would make the game significantly better imo. Anyway you did an absolutely fantastic job with the aesthetics, and this is definitely the most creative idea I've seen this jam.