The opening text on your itch page is genuinely good. "You look down at your hands and see claws" is the kind of opening that makes someone want to play. And the idea of killing in order to not die fits a score game neatly: survival IS the score. The name Bloodscore is a smart welding of the theme to the premise too.

Unfortunately I couldn't get out of the menu. The game loads (Unity), the title screen appears with BLOODSCORE in red and the two buttons, Start Game in lime green and Controls in white, but NEITHER responds. I single clicked, double clicked, focused the canvas first, tried Enter, tried the fullscreen button in the footer. Nothing.

A diagnosis that might help: the entire menu is bunched into the top left corner of the canvas with about two thirds of the screen empty on the right. That's almost always a sign of UI anchored to fixed coordinates, and it tends to be the same root cause as buttons not receiving clicks, because the clickable areas end up somewhere other than where they're drawn. Re-exporting with a responsive canvas and testing in a small browser window would likely fix both at once.

One more thing: your itch page doesn't list the controls, so even if the game had opened I'd have gone in blind. Adding those is two minutes of work.

I couldn't evaluate any of the gameplay, and the premise was one I most wanted to see working. Worth a re-export.