I like where you're going with the general idea. It's almost like a game-wide timer to reach the end. It matches with the theme well.
However, I feel like there isn't any objective for the game in this build ? I killed a variety of enemies, but nothing happened. The different swords have different effects, but they don't seem to truly impact how you play and how you interact with world like you'd expect from a metroidvania.
All of that said, I think it's clear a lot is missing from the game and I'd need to see an updated version to be able to give my full judgment. Keep at it !