As someone who's just made a free puzzle game, I can confidentially tell you some of my own experiences!
Here's some things I had in my game:
1) A grid system where you had to carefully search through air duct vents for wires (items).
To avoid getting electrocuted from touching them, you needed an item that allowed you to view their voltage, so you knew which ones to avoid and which ones you could search in.
2) A mansion with rooms where it was all a relatively condensed area, but it was basically a massive sequence of collecting and gathering items to put in a large "main room" to create a mirror left/right image, and unlock progress.
3) Pushing boxes/rocks into tricky-placed holes to trigger progress.
4) A hedge maze where you had to use sounds and sign hints to guide you to the right path, or else the maze would repeat.
I think something that is often not talked about is that in general, you will almost always have some form of "use key to unlock door" (aka do some task to trigger a switch or variable).
It's just a matter of learning to use different methods of applying that same sort of central idea instead of sticking to bare basics of literal switches and levers.