feat(admin): shell admin + dashboard KPI + recherche ⌘K (Sprint 1)

Layout admin :
- src/app/admin/layout.tsx : route protégée requireRole(ADMIN), sidebar + topbar + breadcrumbs, data-admin sur racine pour theme sobre indépendant du theme public
- Sidebar : 12 sections groupées (Vue d'ensemble, Catalogue, Activité, Membres, Contenu, Système), highlight de la route courante
- TopBar : prompt ⌘K, lien vers site public, email admin
- Breadcrumbs : auto depuis pathname
- CommandPalette : ⌘K / Ctrl K, navigation ↑↓ + Entrée, recherche live debounced 150ms

Dashboard :
- 7 KPI cards avec tone neutral/ok/warn/info (réservations semaine, confirmées 30j, revenus reversés, occupation, nouveaux users, carbets publiés, avis à modérer)
- Section raccourcis fréquents

Theme admin :
- globals.css : [data-admin] override le background+font, neutralise les borders sépia/papier teinté du theme aquarelle, garantit lisibilité permanente

Recherche globale :
- lib/admin/search.ts : query parallèle sur Carbet, User, Booking, ContentPage, PirogueProvider (5 résultats par catégorie, LIKE insensitive)
- api/admin/search?q=… route handler avec requireRole

KPI :
- lib/admin/kpis.ts : 7 métriques live (cache 0), Promise.all, helper formatEur

Pas de dépendance externe ajoutée (cmdk, shadcn) — composants custom Tailwind pour rester léger.

src/lib/admin/kpis.ts

@@ -0,0 +1,101 @@
+/**
+ * KPIs du dashboard admin Karbé.
+ * Toutes les queries sont scoppées à la company (mono-tenant pour l'instant)
+ * et calculent des chiffres simples mais utiles : activité récente, état du
+ * catalogue, modération à faire.
+ */
+
+import "server-only";
+import { prisma } from "@/lib/prisma";
+import { BookingStatus, CarbetStatus, PaymentStatus } from "@/generated/prisma/enums";
+
+export type AdminKpis = {
+  bookingsThisWeek: number;
+  bookingsConfirmed30d: number;
+  revenue30dCents: number;
+  occupancyPct: number; // 0..100
+  newUsers30d: number;
+  publishedCarbets: number;
+  reviewsToModerate: number;
+};
+
+function startOfWeek(d = new Date()): Date {
+  const x = new Date(d);
+  const day = (x.getDay() + 6) % 7; // 0 = lundi
+  x.setHours(0, 0, 0, 0);
+  x.setDate(x.getDate() - day);
+  return x;
+}
+
+function daysAgo(n: number): Date {
+  const x = new Date();
+  x.setHours(0, 0, 0, 0);
+  x.setDate(x.getDate() - n);
+  return x;
+}
+
+export async function getAdminKpis(): Promise<AdminKpis> {
+  const weekStart = startOfWeek();
+  const monthStart = daysAgo(30);
+
+  const [
+    bookingsThisWeek,
+    bookingsConfirmed30dList,
+    newUsers30d,
+    publishedCarbets,
+    reviewsToModerate,
+  ] = await Promise.all([
+    prisma.booking.count({
+      where: { startDate: { gte: weekStart } },
+    }),
+    prisma.booking.findMany({
+      where: {
+        status: BookingStatus.CONFIRMED,
+        paymentStatus: PaymentStatus.SUCCEEDED,
+        startDate: { gte: monthStart },
+      },
+      select: { amount: true, startDate: true, endDate: true },
+    }),
+    prisma.user.count({
+      where: { createdAt: { gte: monthStart } },
+    }),
+    prisma.carbet.count({
+      where: { status: CarbetStatus.PUBLISHED },
+    }),
+    prisma.review.count({
+      where: { hostResponse: null },
+    }),
+  ]);
+
+  const revenue30dCents = bookingsConfirmed30dList.reduce(
+    (acc, b) => acc + Math.round(Number(b.amount) * 100),
+    0,
+  );
+
+  // Occupation = total bookings * jours moyens / (publishedCarbets * 30)
+  // Approximation simple, on raffine en sprint 3.
+  const bookedNights = bookingsConfirmed30dList.reduce((acc, b) => {
+    const diffMs = b.endDate.getTime() - b.startDate.getTime();
+    return acc + Math.max(0, Math.round(diffMs / (1000 * 60 * 60 * 24)));
+  }, 0);
+  const occupancyDen = publishedCarbets * 30;
+  const occupancyPct = occupancyDen > 0 ? Math.min(100, Math.round((bookedNights * 100) / occupancyDen)) : 0;
+
+  return {
+    bookingsThisWeek,
+    bookingsConfirmed30d: bookingsConfirmed30dList.length,
+    revenue30dCents,
+    occupancyPct,
+    newUsers30d,
+    publishedCarbets,
+    reviewsToModerate,
+  };
+}
+
+export function formatEur(cents: number): string {
+  return new Intl.NumberFormat("fr-FR", {
+    style: "currency",
+    currency: "EUR",
+    maximumFractionDigits: 0,
+  }).format(cents / 100);
+}

src/lib/admin/search.ts

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+/**
+ * Recherche globale ⌘K — server function.
+ *
+ * Recherche transversale sur carbets / utilisateurs / réservations /
+ * pages éditoriales / prestataires pirogue. Renvoie au max 5 résultats
+ * par catégorie pour garder la palette lisible.
+ */
+
+import "server-only";
+import { prisma } from "@/lib/prisma";
+
+export type SearchHit = {
+  type: "carbet" | "user" | "booking" | "page" | "provider";
+  id: string;
+  title: string;
+  subtitle?: string;
+  href: string;
+};
+
+export async function adminSearch(query: string): Promise<SearchHit[]> {
+  const q = query.trim();
+  if (q.length < 2) return [];
+  const ci = { contains: q, mode: "insensitive" as const };
+
+  const [carbets, users, bookings, pages, providers] = await Promise.all([
+    prisma.carbet.findMany({
+      where: {
+        OR: [{ slug: ci }, { title: ci }, { river: ci }],
+      },
+      take: 5,
+      select: { id: true, slug: true, title: true, river: true, status: true },
+    }),
+    prisma.user.findMany({
+      where: {
+        OR: [{ email: ci }, { firstName: ci }, { lastName: ci }],
+      },
+      take: 5,
+      select: { id: true, email: true, firstName: true, lastName: true, role: true },
+    }),
+    prisma.booking.findMany({
+      where: { id: ci },
+      take: 5,
+      select: { id: true, status: true, startDate: true, endDate: true },
+    }),
+    prisma.contentPage.findMany({
+      where: {
+        OR: [{ slug: ci }, { title: ci }],
+        lang: "fr",
+      },
+      take: 5,
+      select: { slug: true, title: true, category: true, lang: true },
+    }),
+    prisma.pirogueProvider.findMany({
+      where: { OR: [{ name: ci }] },
+      take: 5,
+      select: { id: true, name: true, rivers: true },
+    }),
+  ]);
+
+  const hits: SearchHit[] = [];
+
+  for (const c of carbets) {
+    hits.push({
+      type: "carbet",
+      id: c.id,
+      title: c.title,
+      subtitle: `${c.river} · ${c.status}`,
+      href: `/admin/carbets/${c.id}`,
+    });
+  }
+  for (const u of users) {
+    hits.push({
+      type: "user",
+      id: u.id,
+      title: `${u.firstName} ${u.lastName}`.trim() || u.email,
+      subtitle: `${u.email} · ${u.role}`,
+      href: `/admin/users/${u.id}`,
+    });
+  }
+  for (const b of bookings) {
+    hits.push({
+      type: "booking",
+      id: b.id,
+      title: `Réservation ${b.id.slice(0, 8)}`,
+      subtitle: `${b.status} · ${b.startDate.toISOString().slice(0, 10)} → ${b.endDate.toISOString().slice(0, 10)}`,
+      href: `/admin/bookings/${b.id}`,
+    });
+  }
+  for (const p of pages) {
+    hits.push({
+      type: "page",
+      id: p.slug,
+      title: p.title,
+      subtitle: `/${p.slug} · ${p.category} · ${p.lang}`,
+      href: `/admin/content-pages/${encodeURIComponent(p.slug)}`,
+    });
+  }
+  for (const p of providers) {
+    hits.push({
+      type: "provider",
+      id: p.id,
+      title: p.name,
+      subtitle: p.rivers.join(" · "),
+      href: `/admin/pirogue-providers/${p.id}`,
+    });
+  }
+
+  return hits;
+}