feat(rust): Economics — pay coins, balances, staff adjust, the richest (PLAN_REDESIGNS §11.2)

The site half of §11.2.2, on protocol 14:

- `rust.coins.pay` ("Pay coins"): irreversible, reversible none (D335). The
  recipient modes of rust.kit.entitle including `linked`, one payment per
  website user (D103's rule), an optional message with {amount}, a new
  `rust.coins` budget. Refused with "Economics is not installed on this
  server" in the dry run too (D199). Core's key goes to the plugin, so a
  retried step answers `repeat` and pays nobody twice.
- `rust_player_wipe_stats.balance`: the tally's balance, written as a value.
  A nameless balance frame (an offline player) moves nobody's last-seen.
  `economics.wiped` clears the wipe's balances, except at a new save.
- The richest: a Coins leaderboard column on one wipe of a server that
  reports Economics, `sort=balance`, and a `richest` title category
  (Magnate); both rank only above the starting balance (D336).
- GET /player/rust/economics (live, falling back to the last known), and
  GET/POST /admin/users/:id/rust/economics for staff — scoped to the user's
  own links, keyed per submission, an activity row with before and after.
- Client: the account page's Coins, the admin user page's Coins panel with
  its form, the leaderboard column, and Economics in the server's mod line
  (saying when its config could not be read).

Server 535/535 (14 new in test/economics.test.js), client 74/74,
routes.manifest regenerated against the pinned core (87 routes), swagger
fragment regenerated.

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

client/src/routes/admin/ChatTitles.jsx

@@ -259,7 +259,23 @@ export function integrationsLine(r) {
       : 'This server’s plugin is older than protocol 12, so it cannot say which optional mods it has.'
   }
   const one = (name, x, without) => (x && x.loaded ? `${name} ${x.version || ''} is loaded`.trim() : `${name} is not loaded — ${without}`)
-  return `${one('BetterChat', r.integrations.betterChat, 'titles and group styles wait for it')}. ${one('PopupNotifications', r.integrations.popupNotifications, 'a popup is refused, and chat still works')}.`
+  const line = `${one('BetterChat', r.integrations.betterChat, 'titles and group styles wait for it')}. ${one('PopupNotifications', r.integrations.popupNotifications, 'a popup is refused, and chat still works')}.`
+  return r.integrations.economics ? `${line} ${economicsLine(r.integrations.economics)}` : line
+}
+
+/**
+ * Economics (PLAN_REDESIGNS §11.2.2), from protocol 14. Its starting balance
+ * decides who the richest column ranks (D336), so a config the plugin could not
+ * read is said: the site then assumes Economics' default of 1000.
+ */
+export function economicsLine(e) {
+  if (!e.loaded) return 'Economics is not loaded — coin rewards, balances and the richest column wait for it.'
+  const name = `Economics ${e.version || ''}`.trim()
+  if (e.startingBalance === undefined || e.startingBalance === null) {
+    return `${name} is loaded, but its config could not be read — the site assumes a starting balance of 1,000.`
+  }
+  const wipes = e.wipesWithMap === true ? 'balances wipe with the map' : e.wipesWithMap === false ? 'balances carry over a wipe' : null
+  return `${name} is loaded — starting balance ${Number(e.startingBalance).toLocaleString()}${wipes ? `, ${wipes}` : ''}.`
 }
 
 export function VoiceCard() {