I'm a bit torn on how to score your game. It's very well done as always, and the creative take on what a pet to care for meant in your game is handled very well. At the same time, progression feels a bit forced, and other than having an in game pet, I'm not sure what tamagotchi elements you have. However, I want you to keep going in this direction. pets existed in gladiator battles, and I think this adds a fun additional mechanic to the gameplay.
I would say "having more ways to care for the pet would make progression feel more meaningful" and that is true, but I think that would take away too much from the incredible game you're already working on. This is one of those catch 22 situations where if you focus more on scoring well, your game would move in a weird direction, but if you continue to make your game what you want (which is the right choice imo) Then you might get low scores, but a better game.
TLDR I love this game, I love the direction you're going, even if you get eliminated, you're a champ in my book. Great job bro.