Polish FixMap public launch examples

[aryamthecodebreaker]

Summary

• Fixes GitHub Action input reading for dashed inputs like github-token, while keeping shell-safe underscore fallback support.
• Adds a tiny auth example repo and sample FixMap report so public visitors can try the MVP quickly.
• Adds a public launch checklist and links the example from the README.

Verification

• npm run build:action
• npm run ci
• node packages/cli/dist/cli.js plan --issue "password reset emails fail" --repo examples/tiny-auth-app
• npm audit --audit-level=moderate (found 0 vulnerabilities)
• git diff --check

Notes

This keeps the repository private/public setting unchanged; Aryam said he is making it public separately.