Whereas if you try to fit the world into the puzzles, you’d end up with uneven world.
I usually begins with the plot/story. Then I see what Rooms/Objects/Persons are involved. Make some kind of lists, and go from there.
I’d draw the rooms on the map bigger (either yellow pad or index card), so I can fit in objects there. Add ObjectId, and make a list somewhere for properties. It makes for a clean map, albeit a bit ponderous as you go back and forth between maps, objects, and notes.
My technique is not dissimilar. Setting plays a big part. Where the game is set and also when the game is set. Since most of my puzzles are of the medium-sized-dry-goods variety it helps to think about what sort items one might encounter in that place in that time period. I’ll write down a few ideas for objects and often one object will speak to another and suggest a possible puzzle involving both.
Research is invaluable for enriching a setting, particularly when writing a historical game. Primary sources for preference. I didn’t know, for instance, that Victorian balloonists really did take animals and musical instruments up in their balloons with them, that pirates ate flamingos and considered them a delicacy, or what a torsion wrench was. If I’m stuck for ideas I’ll go back to my books and often something will suggest itself.