feat(engagement): Admin - Engagement - Rules and Audiences (engagement Phase 4b)

The admin surface over the Phase 4a engine: two screens, twelve routes and the
reach preview. Nothing in the engine changed; what changed is that an operator
can now reach it.

Four decisions settled by the org lead before any code:

  - segments get their OWN nav entry, "Audiences", not a tab of the rules screen
  - the on/off switch is its own PATCH route, not a full PUT
  - the reach preview is a count only, on demand
  - a rule can be hard-deleted; the send log survives it

The switch is the one with real content in it. A PUT re-validates against the
registries as they are NOW, so the rules a re-validating toggle cannot switch
off are exactly the three an operator most wants stopped: a rule whose module
was uninstalled, one naming a channel that is gone, and one whose trigger has
since narrowed its ceiling under a saved audience. PATCH .../enabled writes one
column and always works. Switching ON unvalidated is safe because the engine
re-checks the ceiling at send time.

The preview calls the engine's own resolver rather than a second query that
agrees with it today, and answers a count and nothing else - the resolver's
output for a module-declared segment is a set of players derived from game data.
It reports `capped` at the 5000-row bound (the count is a floor, not a total),
`reason` for an `owner` audience (which resolves per event and has no advance
answer), and `permitted` so the editor cannot show a healthy number beside a
save the server will refuse.

Two defects found by walking it against a live server, both in Phase 4a's code:

  1. A rule pointing at a DORMANT segment read as healthy. listAnnotated asked
     only whether the segment ROW existed. The other shape of the same failure
     is a segment sitting exactly where it was whose every audience belongs to
     an uninstalled module: same outcome, nothing deleted. Uninstalling a module
     under an enabled rule produced a rule the screen showed as on and firing.
     The expression walk now lives in engagement/segments.js as
     `missingAudiences` and both lists ask it.
  2. "1 rule still use this segment" - the delete refusal pluralised the noun
     and not the verb, in the sentence an operator reads when told no.

Also: a rule's trigger is now a stated rule rather than an omission in the
UPDATE statement (its cooldowns, queued sends and history are all about one
trigger id); a condition tree the editor cannot render is shown read-only rather
than flattened, because flattening changes which events fire the rule; and
literals are coerced client-side to the type the trigger declared, with anything
that does not parse passed through unchanged so the server's refusal names the
variable.

Tests: 21 new server tests (test/engagementAdmin.test.js) and 25 client ones
(client/test/engagementRules.test.js), all green. The single failure in the
server suite (`the committed manifest matches the declarations in the tree`) is
the known Windows CRLF artifact and fails identically on clean edge.

Companion docs PR: docs#184.

- [x] AI-assisted: written with Claude Code (Opus)

Co-Authored-By: Claude <noreply@anthropic.com>

client/src/App.jsx

@@ -42,6 +42,8 @@ import UsersAdmin from './routes/admin/views/UsersAdmin.jsx'
 import UserDetail from './routes/admin/views/UserDetail.jsx'
 import InvitesAdmin from './routes/admin/views/InvitesAdmin.jsx'
 import ModulesAdmin from './routes/admin/views/ModulesAdmin.jsx'
+import EngagementRules from './routes/admin/views/EngagementRules.jsx'
+import EngagementAudiences from './routes/admin/views/EngagementAudiences.jsx'
 import TeamsAdmin from './routes/admin/views/TeamsAdmin.jsx'
 import AccountAdmin from './routes/admin/views/AccountAdmin.jsx'
 import Moderation from './routes/admin/views/Moderation.jsx'
@@ -184,6 +186,22 @@ export default function App() {
                   actions that publish a game-written name is applied per request
                   on the server, from the caller's live role (TEAMS.md 2.9). */}
               <Route path="teams" element={<TeamsAdmin />} />
+              {/* Engagement (ENGAGEMENT.md Phase 4b). Admin-only, matching the
+                  server: every route under /admin/engagement re-gates to `admin`
+                  on top of the group's staff gate, because this is the group that
+                  decides who receives mail. */}
+              <Route
+                path="engagement"
+                element={
+                  <RoleGate roles={['admin']}>
+                    <Outlet />
+                  </RoleGate>
+                }
+              >
+                <Route index element={<Navigate to="rules" replace />} />
+                <Route path="rules" element={<EngagementRules />} />
+                <Route path="audiences" element={<EngagementAudiences />} />
+              </Route>
               <Route path="account" element={<AccountAdmin />} />
               {/* Installed modules' admin pages, at /admin/<id>/…, already inside
                   RequireAuth + AdminLayout. A module cannot supply its own auth