Cost-engineering an "AI Generate" button in a freemium product (from $0.08 to $0.029 per click)

TL;DR My coding-interview prep app has a "Generate Visualization" button . Click it on any algorithm problem and Claude Sonnet 4.5 produces a self-contained interactive widget that teaches it — a sliding-window expanding, a two-pointer racing, a DP table filling cell by cell. (That's what the GIF above is showing.) At naive implementation, each click cost me about $0.08 . Workable for Pro subscribers. Ruinous if I let free-tier users click freely. Through five cost decisions — tiering the call p