Ah - I forgot I had comments disabled on that one. (Since it's no longer April Fools' Day 2023 I've opened them up now!)
I recall the issue with levels being skipped only emerged once I uploaded the browser version to itch. I suspect it's down to the end of each level being triggered based on when certain audio finishes playing, and those triggers sometimes activating because the browser version hasn't yet loaded the audio rather than because it's played and stopped.
Long story short: I don't have time to dig in and fix it the underlying problem right now, but if you try a downloadable version of the game it's likely to work better.