Thank you!!
I think one way to approach puzzle design is to design around two naturally contradictory things, since this can quite quickly turn into complexly coupled mechanics. In our case, the initial pitch for the game was "Each doohickey can be solved by rotating its orientation on the vault, but by doing this you also rotate all other doohickeys, potentially unsolving them." Then from there it was just experimenting to see what specific mechanics would lean into that idea the best!
But that's just a rough outline of how we designed this game, there are countless ways to go about it :)