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

package.json

@@ -29,7 +29,7 @@
     "check:csp": "node scripts/checkCsp.mjs",
     "play:datasafety": "node scripts/playDataSafety.mjs",
     "beta": "node scripts/beta.mjs",
-    "test": "node --test test/beta.test.mjs test/legal.test.mjs test/footer.test.mjs",
+    "test": "node --test test/beta.test.mjs test/legal.test.mjs test/footer.test.mjs test/demo.test.mjs",
     "brand:assets": "node scripts/buildBrandAssets.mjs",
     "screens:capture": "node scripts/captureScreens.mjs",
     "csp:hashes": "node scripts/checkCsp.mjs --reset && astro build && node scripts/checkCsp.mjs --write && astro build && node scripts/checkCsp.mjs",