The Library as Adventure
A library trip isn't an errand. It's a treasure hunt with no wrong answers.
Let the kid wander. Let them pull books off shelves based on the cover (that's literally what adults do). Let them pick too many, the library doesn't charge by the pound. Don't hover. Don't redirect. Don't say "how about something a little harder?" The goal is for the library to feel like a place where they have power, choices, and unlimited free books.
Pro tip: many libraries let kids get their own library card starting at age 5-6. The card itself is a milestone, a physical object that says "I am a person who reads." Kids who have their own library card use it. The ownership matters.