CI/CD: Auto-deploy demo site on merge to `main`

[lattln]

Description

Set up GitHub Actions to build and deploy the demo application so that main always reflects the latest working demo.

Currently the repo exposes demo functionality via npm run dev:demo. A production-compatible demo build and deploy flow is needed.

Scope

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• Add or formalize a build:demo script if missing
• Trigger deployment on push to main
• Build demo app in CI (no dev server)
• Deploy demo to:
  • GitHub Pages sub-path or
  • separate demo deployment target

Acceptance Criteria

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• Demo URL always reflects latest main
• Demo build is reproducible in CI (no local env assumptions)
• README documents the public demo URL