[schloerke]

Front-page fixes from user feedback:

• The JavaScript tab is titled ui.tsx (it uses JSX), highlighted as jsx.
• The mount call appends its own container to <body> — there is no #root in a set_react_page() / page_react() page, so the old getElementById("root") was null.
• An Agent Skills section sits directly below Installation.
• The skills double as the starter template: the front page and both agent-skills articles carry a paste-ready prompt for /shinyreact-build-app (Python / R variants), plus a one-line /shinyreact-convert-app example. Addresses the "obvious place for a starter template" feedback without a second copy of the Vite config to drift.