That's the thing, clicking Begin Night sent be back into Night 1. I just tested the game again and had the same issue (Firefox), but when I tried it in Safari, it worked!
Something funky is going on with Godot web builds. Our game has some screen effect issues on macOS using Chrome and Safari but not in Firefox. Seems like some Godot games and different browsers have different ideas of how they should work when running on macOS, as our issues disappear on Windows and Linux. Weird as! I'll give it another go on Safari now that I know it is a browser compatibility issue.