docs: document /public version+brand; mark PLAN §8 items 4 & 6 done

Counterpart to RunicGateway/website#77.

- BACKEND_DESIGN.md: /public table now documents the new GET /public/version
  (DB-free identity/version), the version block on /public/status, and the brand
  block on /public/settings (per-shard theming: name/accent/logo/hero/favicon).
- android/PLAN.md: mark §8 item 4 (version/health) and item 6 (branding) DONE and
  update the prerequisite-progress summary — all v1 prerequisites are now done;
  only push notifications (item 3) remains and is post-v1 (M7). App M0–M4 unblocked.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NgyHnrNa8WwG3doxvxjuCr

website/BACKEND_DESIGN.md

@@ -195,8 +195,9 @@ by `seed.js` from env (see §6); further staff are created under `/admin/users`
 ### /public  (public.routes.js → public.controller.js) — all GET, no auth
 | Method | Path | Notes |
 |---|---|---|
-| GET | `/settings` | whitelisted public keys only (mode, maintenance_message, status_message, homepage_teaser, contact_email, site_title) |
-| GET | `/status` | status message + current mode |
+| GET | `/settings` | whitelisted public keys, derived `registration`/`gameAccountSignup` flags, and the per-shard **`brand`** block (name, `accent` color, logo/hero/favicon) a client themes itself from — one image runs as any shard. Asset fields may be site-relative paths (resolve against the base URL). |
+| GET | `/status` | status message + current mode, **plus a `version` block** (`{ service:'runic-gateway', api, server }`) so a client first-run probe recognizes the backend and can run a version-mismatch guard |
+| GET | `/version` | lightweight, **DB-free** backend identity/version (`{ service, api, server }`) — the canonical target for the version guard and a cheap liveness check |
 | GET | `/posts/:category` | published only; `category` ∈ news\|five-on-friday\|newsletter\|screenshots |
 | GET | `/posts/:category/:idOrSlug` | single published post |
 | GET | `/wiki` | list of pages (slug + title) |