docs(experiments): capture rendered entrypoint output and UI walkthrough

Demonstrates the new CLAUDE/CODEX/GEMINI system-prompt overrides and the
CODEX_EXTRA_SKILLS_PATHS hook. The .ts/.mjs renderers reproduce the
files written into ~/.claude, ~/.codex, ~/.gemini at container start so
reviewers can compare default vs overridden output without spinning up
a container.

Author: konard