Yeah, I had a similar experience watching a friend try to figure my game out on a call a few hours before the deadline like... "oh yeah, I didn't really explain half of this stuff, huh?" 😅 For a puzzle game it's got to be doubly true! Fresh eyes from playtesting is very valuable. I think this little known channel called GMTK may also have some vids on puzzle games which may help.
Did you ever play The Witness? I think that game makes it really obvious because they literally use puzzle familiarity like a metroidbrainia gating system. Like there's nothing stopping you exploring a late game area from the start since all puzzles are solvable in isolation, except the puzzles are too hard because you haven't found the ones that let you have the "aha" moments yet. The fact that that principle can be used to gate exploration in such an effectively-rigid way is very eye-opening for just how crucial those "teaching" puzzles are!