fix: FastAPI owns root, mount Gradio at /gradio, fix API path in index.html

fix: absolute URL for API calls from /game context

fix: /game serves index.html, correct API path /gradio_api/run/

debug: try both API paths, show full response

debug: show real error in startDungeon alert

fix: serve index.html via demo.app route, Gradio at root

fix: FastAPI serves index.html at root, Gradio API at /gradio/run/*

fix: full static HTML UI + pure Gradio API backend, bypass gr.HTML entirely

fix: connect Play buttons to live HF Space

deploy: landing page as index.html on main