feat(web): admin backoffice — meshes, sessions, invites, audit, overview

Four new admin routes backed by the mesh API modules:

- /admin/meshes — paginated data-table (name, owner, tier, transport,
  members, created). Tier + transport multiSelect filters.
- /admin/meshes/[id] — detail page: owner row + 4 live sections
  (members, presences, invites, last 50 audit events).
- /admin/sessions — live Claude Code WS presences. Status filter,
  pulse dot for working sessions, disconnected badge.
- /admin/invites — invite tokens w/ status derived client-side
  (active/revoked/expired/exhausted).
- /admin/audit — metadata-only event log, event-type + mesh + date
  filters.

Overview page at /admin rewritten to 6 summary cards (users, orgs,
customers, meshes, sessions, messages 24h) joining the base
/admin/summary and /admin/summary/mesh endpoints.

Sidebar navigation gains a second "mesh" group with the four new entries.
paths.ts extended with admin.meshes / sessions / invites / audit.

All UI reuses @turbostarter/ui-web/data-table — columns.tsx + thin
*-data-table.tsx wrapper per the existing users pattern.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/web/src/app/[locale]/admin/audit/page.tsx

@@ -0,0 +1,85 @@
+import {
+  createSearchParamsCache,
+  parseAsArrayOf,
+  parseAsInteger,
+  parseAsString,
+} from "nuqs/server";
+import { Suspense } from "react";
+
+import { getAuditResponseSchema } from "@turbostarter/api/schema";
+import { handle } from "@turbostarter/api/utils";
+import { pickBy } from "@turbostarter/shared/utils";
+import { DataTableSkeleton } from "@turbostarter/ui-web/data-table/data-table-skeleton";
+
+import { api } from "~/lib/api/server";
+import { getMetadata } from "~/lib/metadata";
+import { AuditDataTable } from "~/modules/admin/audit/data-table/audit-data-table";
+import { getSortingStateParser } from "~/modules/common/hooks/use-data-table/common";
+import {
+  DashboardHeader,
+  DashboardHeaderDescription,
+  DashboardHeaderTitle,
+} from "~/modules/common/layout/dashboard/header";
+
+const searchParamsCache = createSearchParamsCache({
+  page: parseAsInteger.withDefault(1),
+  perPage: parseAsInteger.withDefault(50),
+  sort: getSortingStateParser().withDefault([
+    { id: "createdAt", desc: true },
+  ]),
+  q: parseAsString,
+  eventType: parseAsArrayOf(parseAsString),
+  meshId: parseAsArrayOf(parseAsString),
+  createdAt: parseAsArrayOf(parseAsInteger),
+});
+
+export const generateMetadata = getMetadata({
+  title: "Audit · Admin",
+  description: "Audit log of mesh events.",
+});
+
+export default async function AuditPage(props: {
+  searchParams: Promise<Record<string, string | string[] | undefined>>;
+}) {
+  const searchParams = await props.searchParams;
+  const { page, perPage, sort, ...rest } =
+    searchParamsCache.parse(searchParams);
+
+  const filters = pickBy(rest, Boolean);
+
+  const promise = handle(api.admin.audit.$get, {
+    schema: getAuditResponseSchema,
+  })({
+    query: {
+      ...filters,
+      page: page.toString(),
+      perPage: perPage.toString(),
+      sort: JSON.stringify(sort),
+    },
+  });
+
+  return (
+    <>
+      <DashboardHeader>
+        <div>
+          <DashboardHeaderTitle>Audit log</DashboardHeaderTitle>
+          <DashboardHeaderDescription>
+            Metadata-only event log — no message content, only routing.
+          </DashboardHeaderDescription>
+        </div>
+      </DashboardHeader>
+      <Suspense
+        fallback={
+          <DataTableSkeleton
+            columnCount={5}
+            filterCount={2}
+            cellWidths={["8rem", "10rem", "8rem", "8rem", "10rem"]}
+            shrinkZero
+          />
+        }
+      >
+        <AuditDataTable promise={promise} perPage={perPage} />
+      </Suspense>
+    </>
+  );
+}