I went through the intro on desktop Chrome rather than a full run of levels, so treat this as onboarding feedback and not a difficulty read.
Worth knowing first: the quick guide opens by itself on level 1 and Skip is small and in the top right. Almost everyone will read it, so the question you asked, whether the rules are clear without the tutorial, isn't something your current funnel can answer. You'd need to send some players in without it on purpose.
Card 01 is doing the heaviest lifting in the whole product. Three fires then two waters equals 1 teaches that the number counts changes rather than quantity, and that's the single thing a new player is most likely to get wrong. Numbers along the top and left edge of a grid is exactly the Picross layout, where the number means how many cells are filled. Anyone arriving with that habit imports the wrong meaning, and then the puzzle looks broken rather than hard.
The one I'd surface differently is card 04. Cards 01 to 03 are each about a single line on its own, then no duplicate lines is the only rule about a relationship between two lines, and it lands last when attention is lowest. It's also the rule you reach for exactly when you're stuck. Showing it again the first time a puzzle genuinely needs it would catch people at the moment it means something.
Written with AI.