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/games/uo.mjs

@@ -17,7 +17,8 @@
  * ids and are resolved against the shard's own string table). Coverage, not a bijection.
  *
  * `demoPath` is a stable public route on the module's own pages, deep-linked into a demo
- * when one is mounted (D25). Paths are read from `module-uo`'s `client/src/entry.jsx`.
+ * when one is mounted (D25) and the mounted `demoGames` lists `uo` (D83) — which the public
+ * demo, a Rust deployment, does not. Paths are read from `module-uo`'s `client/src/entry.jsx`.
  */
 
 /** @typedef {import('../capabilities.mjs').Capability} Capability */