feat(auth): add Supabase auth with Google, GitHub, and email OTP login

Introduce user registration/login gated behind optional NEXT_PUBLIC_SUPABASE_*
env vars (leave blank to disable — app behaves exactly as before). Adds
proxy.ts for automatic cookie session refresh, requireUser() API route
guards on all 7 compute-consuming routes, AuthModal (Google/GitHub OAuth +
6-digit email OTP), UserChip header component, and login_success analytics
event. Identity is fully decoupled from Session/engine — no type changes.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

package.json

@@ -20,6 +20,8 @@
     "deploy:cf": "opennextjs-cloudflare deploy"
   },
   "dependencies": {
+    "@supabase/ssr": "^0.12",
+    "@supabase/supabase-js": "^2.108",
     "jsonrepair": "^3.14.0",
     "jszip": "^3.10.1",
     "next": "^16.0.0",