Wire production API origin for public demo (CORTEX_API_ORIGIN)

[cursor]

Background

Public dashboard is live on Vercel, but Ask/search is not API-backed until the backend origin is configured.

Problem Statement

/health (and query paths) return 503 / fail until CORTEX_API_ORIGIN points at a deployed API (Render / Plan A).

Proposed Solution

1. Deploy API per docs/DEPLOY-FREE.md or docs/DEPLOY.md
2. Set CORTEX_API_ORIGIN on Vercel
3. Verify with ./scripts/verify_free_deploy.sh --api … --pages …

Acceptance Criteria

• Public dashboard Ask returns real graph results for workspace local-dev (or demo workspace)
• /health via the public pages/proxy is healthy
• Verification script (or equivalent smoke) documented in PR/issue comment

Files / Modules Affected

docs/DEPLOY-FREE.md, docs/DEPLOY.md, Vercel env, Render/render.yaml

Related: Phase 7 closeout ops (no video/launch announcement).