feat(demo): list the demo's sign-ins on /beta and link into it per game

The public demo (demo.runicgateway.com) is live, so the site's demo slot
can be switched on. Two decisions of record, PLAN.md §15:

- D82: /beta reads the demo's GET /api/v1/public/settings demo.logins on
  the server, caches it for a minute, and lists the published sign-ins
  with the next wipe. If the demo does not answer, /beta links to its
  sign-in page instead. Gate two reads as in place.
- D83: a deep link into a game module's pages carries data-demo-game, and
  applyBrand.mjs fills it only for games in the new mounted demoGames
  list. The Rust features gain links into /rust and /rust/servers/demo.
  UO's stay hidden on a Rust demo.

The public-demo not-built entry is removed, because its resolvedBy was met.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01E14m6SuuY6i1vASFeGDBeY

src/data/beta.mjs

@@ -32,9 +32,9 @@
  *   2. SOMEWHERE TO POINT IT. `ConnectScreen.kt` on `Android-app` `main` is blunt about
  *      this — "nothing else in the app runs until a valid Runic Gateway site is entered and
  *      validated". An installed app with no deployment behind it is a text field. D27 makes
- *      the public demo (§15) the tester target rather than naming a private shard, which
- *      means the beta opens when the demo VM does. `notBuilt.mjs` already carries that
- *      absence; this page renders the demo link from `demoUrl` when there is one.
+ *      the public demo (§15) the tester target rather than naming a private shard. The demo
+ *      went up on 2026-10-27; with `demoUrl` mounted, `/beta` marks this gate in place and
+ *      lists the demo's sign-ins as the demo publishes them (D82, `lib/demoLogins.mjs`).
  *
  * Neither gate is a reason not to collect addresses now — the list is what makes the first
  * batch possible on day one — but a page that hid them would be advertising a beta that
@@ -180,8 +180,7 @@ export const requirements = [
     body:
       'The app ships pointed at nothing. Its first screen asks for the address of a site ' +
       'running this platform and validates it before anything else in the app will run — ' +
-      'so a tester needs either their own deployment or the public demo, which is the ' +
-      'second of the two things this beta is waiting on.',
+      'so a tester needs either their own deployment or the public demo.',
   },
 ];