I'm running at the high end of mid-range rigs. Tried via Chrome, Firefox and Edge. I was able to interact with the main menu but couldn't move the player character once the next scene loaded in. Audio still plays in.
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I think that's what's up. Godot doesn't do particle caching, it compiles them at run time. I thought this may be the case so I let the game run for a bit longer and it started behaving as intended. I'd put a note up on one of your pages giving folks the heads up that it takes a bit to load shaders and will eventually work as intended!
Now that I've seen it, well done! It delivered like I'd hoped it would!