I have a design for the lower-level / core gameplay mechanics of a game, and a prototype for them. They feel pretty good.
Good. Stop right there before going any further. Are you able to produce a noteworthy collection of puzzles out of that? Yes, I am asking you to first do the thing you try to avoid, a collection of levels. This is important for two reasons.
1. To verify/explore the potential of the gameplay-mechanics.
2. To shape a profound understanding about puzzle design. This can already be obtained by concentrating on a collection of levels, as the principles remain the same, regardles to which level you apply them.
People who struggle with high-level puzzle design are those who don't understand low-level either. So I strongly advise to get experienced with point 2 first, as suggested. I actually consider to provide a formal introduction to puzzle-theory which I developed along the way, when I get to it. That will reveal the possible structure and properties of puzzles. And that will empower your creativity indefinitely, as it will profoundly help you to recognize the structure behind the most crazy things.
I previously only released games to the public which are essentially just a collection of puzzles. And I now leverage my knowledge to create a grand organic adventure about AI-revolution. From an abstract high-level perspective, it's still a (giant) puzzle with various interlocked subsystems.