This is awesome. Launching yourself around with the sword is so much fun, all of the platforming was so satisfying, and there's amazingly little jank for such a nonstandard physics based mechanic. The combat felt a bit less developed than the platforming but was still really satisfying - using the sword to block lasers is such a cool idea and really helps go the extra mile to selling the physicality of the whole system. It was also a lot of fun to combo the boss with the spin attack, though the boss was just a little frustrating before I discovered that due to spending so much time offscreen. It's kind of a lazy solution but I wonder if a little indicator arrow for when it goes offscreen would help keep track of it without needing to shrink down the arena or tone done the shotgun attachment, as doing either of those would detract from the spectacle a bit I feel.
The only clear issue I noticed was the save system didn't actually seem to save anything but the player position, and it didn't actually save to file (I was forced to start over when I accidentally reloaded the page - thankfully after only reaching one save point). I don't know if it can even really be called a save system in this state, they're effectively just checkpoints. I also notice you mention crafting in the description, but I honestly don't see what a crafting system would add to this game, especially if its a bog standard menu based system. Keeping the upgrades as simple pickups seems fine to me.