fix: resolve 2026-03-04-lzdy branch conflicts — Dr. Bot branding, credential fallback, new scripts

[Copilot]

The 2026-03-04-lzdy branch diverged from main with improvements that couldn't cleanly merge. This PR cherry-picks the meaningful changes onto the current main base, resolving conflicts.

beauty-assistant edge function

• Dr. Bot rebranding: system prompt updated from "You are the **Asper Dual-Voice Concierge**..." → "You are **Dr. Bot** — the Asper Dual-Voice Concierge..."
• Credential fallback: removed non-null assertions on Supabase env vars; product context fetch now skips gracefully when SUPABASE_URL/SUPABASE_SERVICE_ROLE_KEY are absent:

  // Before — throws at runtime if env vars missing
  const serviceClient = createClient(Deno.env.get("SUPABASE_URL")!, Deno.env.get("SUPABASE_SERVICE_ROLE_KEY")!);
  
  // After — skips product context when credentials absent
  const supabaseUrl = Deno.env.get("SUPABASE_URL");
  const supabaseServiceKey = Deno.env.get("SUPABASE_SERVICE_ROLE_KEY");
  if (supabaseUrl && supabaseServiceKey) { /* fetch products */ }

• Added JSDoc header, declare const Deno declaration, and // @ts-expect-error annotations for Deno URL imports
• Renamed "Sales & Trust" section → "Trust & Authenticity"

CI workflow fixes

• azure-webapps-node.yml: added if: secrets.AZURE_WEBAPP_PUBLISH_PROFILE != '' — was failing on every main push due to unconfigured Azure credentials and placeholder your-app-name
• sync-file-changes-to-lovable.yml / sync-issues-prs-to-lovable.yml: curl webhook calls now use || echo fallback so a non-responsive Lovable endpoint doesn't fail the workflow

New files from lzdy branch

• scripts/brain-check.js — Beauty Assistant (edge function) connectivity check (npm run brain)
• scripts/sync-check.js — combined frontend + brain health check (npm run sync:check)
• skills/code-connect-components/SKILL.md, skills/get-pr-comments/SKILL.md, .agents/skills/code-connect-components/SKILL.md, skills-lock.json — Cursor skill definitions

package.json / README

• Added health, brain, sync:check scripts; preserved existing sync/sync:dry/sync:publish (Shopify catalog) scripts
• Added scripts reference table and Sync Check docs to README

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