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

server/db/schema.sql

@@ -1363,3 +1363,11 @@ CREATE TABLE IF NOT EXISTS rust_npc_factions (
 -- stage 4, D250). Null for every other stat. No foreign key: a deleted profile
 -- leaves a rule that ranks nobody, which the form shows and an admin removes.
 ALTER TABLE rust_title_rules ADD COLUMN IF NOT EXISTS profile_id INT UNSIGNED NULL;
+
+-- Economics (PLAN_REDESIGNS §11.2.2, D336): a player's last known coin balance
+-- on the server, for the wipe it was reported in. A VALUE, written over, never
+-- summed — the tally carries the balance itself, not a change. NULL until the
+-- server has reported one, and again after `ecowipe` clears the wipe's. The
+-- richest column and the Magnate title rank only balances above the server's
+-- starting balance, so the untouched accounts of a fresh wipe rank nobody.
+ALTER TABLE rust_player_wipe_stats ADD COLUMN IF NOT EXISTS balance DECIMAL(14,2) NULL;