feat(09-01): add classification API route, client hook, badge component, and setup detail wiring

- Add PATCH /:id/items/:itemId/classification endpoint with Zod validation
- Add apiPatch helper to client API library
- Add useUpdateItemClassification mutation hook
- Add classification field to SetupItemWithCategory interface
- Create ClassificationBadge click-to-cycle component (base/worn/consumable)
- Wire ClassificationBadge into setup detail page item grid
- Add integration tests for PATCH classification route (valid + invalid)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/client/hooks/useSetups.ts

@@ -1,5 +1,5 @@
 import { useMutation, useQuery, useQueryClient } from "@tanstack/react-query";
-import { apiDelete, apiGet, apiPost, apiPut } from "../lib/api";
+import { apiDelete, apiGet, apiPatch, apiPost, apiPut } from "../lib/api";
 
 interface SetupListItem {
 	id: number;
@@ -24,6 +24,7 @@ interface SetupItemWithCategory {
 	updatedAt: string;
 	categoryName: string;
 	categoryIcon: string;
+	classification: string;
 }
 
 interface SetupWithItems {
@@ -105,3 +106,20 @@ export function useRemoveSetupItem(setupId: number) {
 		},
 	});
 }
+
+export function useUpdateItemClassification(setupId: number) {
+	const queryClient = useQueryClient();
+	return useMutation({
+		mutationFn: ({
+			itemId,
+			classification,
+		}: { itemId: number; classification: string }) =>
+			apiPatch<{ success: boolean }>(
+				`/api/setups/${setupId}/items/${itemId}/classification`,
+				{ classification },
+			),
+		onSuccess: () => {
+			queryClient.invalidateQueries({ queryKey: ["setups", setupId] });
+		},
+	});
+}