The blocky movement and combat reminded me a bit of Prince of Persia 3D, so I think you really nailed the theme. And making a 3D game for a jam is a ton of work, so great job!
I noticed you mentioned that progress doesn't save in the web version. I don't know how you're currently saving player data, but here's a tip: if you use user://app_data/ instead of res://app_data/ as the root folder, the downloaded version will store the data in the user's AppData folder, which is where it should go. And in the browser, it'll be stored in the browser's local storage/cache automatically.
That's how I handled saves in my game, and it works really well. You might want to give it a try—and feel free to test it in my game too! :)