Repair landing navigation wiring and add end-to-end Google sign-in support

[Copilot]

landing.html was pointing to a non-existent auth.html, which broke Registration/Sign In/Request Access flows and disconnected users from the actual auth surface. This updates navigation wiring and introduces a working Google sign-in path that mints platform JWTs.

• Landing navigation + access entrypoints

  • Replaced broken auth.html links with index.html hash routes:
    • Registration -> index.html#register
    • Sign In -> index.html#signin
    • Request Access -> index.html#register
  • Added Privacy Policy to the same top menu action box as Registration / Sign In / Book Demo.

• Frontend auth UX (frontend/index.html)

  • Added hash-aware auth mode switching for #signin and #register.
  • Added a Google sign-in CTA in the auth card.
  • Added Google config bootstrap from backend (/auth/google/config).
  • Hardened JWT payload parsing for offline/sim mode fallback (format checks + safe decode path).

• Backend Google auth integration (backend/apps/api-gateway)

  • Added GET /auth/google/config to expose whether Google sign-in is enabled and the configured client ID.
  • Added POST /login/google:
    • verifies Google ID token via Google tokeninfo
    • enforces verified email and audience match (GOOGLE_CLIENT_ID) when configured
    • upserts login path by creating a user on first Google login
    • returns existing Prexus auth response shape (token + user).

• Config surface

  • Added GOOGLE_CLIENT_ID to .env.example for explicit OAuth configuration.

Example of the fixed landing wiring:

<a href="index.html#register" class="menu-item">Registration <span class="arr">→</span></a>
<a href="index.html#signin" class="menu-item">Sign In <span class="arr">→</span></a>
<a href="privacy-policy.html" class="menu-item">Privacy Policy <span class="arr">→</span></a>