Both the buttons stayed down I'm not sure if this is intended but I couldn't get past it.
Poke Toade. :)
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There are two kinds of buttons, the ones without a brim will stay down once stepped on. I should make them more distinct I see, thanks for the comment. The level can be beaten! You can restart it from the menu in the bottom right or by pressing R.
EDIT: Updated the game. Both kinds of buttons are very different from one another now.