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/routes/setups/$setupId.tsx

@@ -1,12 +1,14 @@
 import { createFileRoute, useNavigate } from "@tanstack/react-router";
 import { useState } from "react";
 import { CategoryHeader } from "../../components/CategoryHeader";
+import { ClassificationBadge } from "../../components/ClassificationBadge";
 import { ItemCard } from "../../components/ItemCard";
 import { ItemPicker } from "../../components/ItemPicker";
 import {
 	useDeleteSetup,
 	useRemoveSetupItem,
 	useSetup,
+	useUpdateItemClassification,
 } from "../../hooks/useSetups";
 import { useWeightUnit } from "../../hooks/useWeightUnit";
 import { formatPrice, formatWeight } from "../../lib/formatters";
@@ -24,6 +26,7 @@ function SetupDetailPage() {
 	const { data: setup, isLoading } = useSetup(numericId);
 	const deleteSetup = useDeleteSetup();
 	const removeItem = useRemoveSetupItem(numericId);
+	const updateClassification = useUpdateItemClassification(numericId);
 
 	const [pickerOpen, setPickerOpen] = useState(false);
 	const [confirmDelete, setConfirmDelete] = useState(false);
@@ -86,6 +89,12 @@ function SetupDetailPage() {
 		}
 	}
 
+	function nextClassification(current: string): string {
+		const order = ["base", "worn", "consumable"];
+		const idx = order.indexOf(current);
+		return order[(idx + 1) % order.length];
+	}
+
 	function handleDelete() {
 		deleteSetup.mutate(numericId, {
 			onSuccess: () => navigate({ to: "/setups" }),
@@ -208,18 +217,32 @@ function SetupDetailPage() {
 									/>
 									<div className="grid grid-cols-1 md:grid-cols-2 lg:grid-cols-3 gap-4">
 										{categoryItems.map((item) => (
-											<ItemCard
-												key={item.id}
-												id={item.id}
-												name={item.name}
-												weightGrams={item.weightGrams}
-												priceCents={item.priceCents}
-												categoryName={categoryName}
-												categoryIcon={categoryIcon}
-												imageFilename={item.imageFilename}
-												productUrl={item.productUrl}
-												onRemove={() => removeItem.mutate(item.id)}
-											/>
+											<div key={item.id}>
+												<ItemCard
+													id={item.id}
+													name={item.name}
+													weightGrams={item.weightGrams}
+													priceCents={item.priceCents}
+													categoryName={categoryName}
+													categoryIcon={categoryIcon}
+													imageFilename={item.imageFilename}
+													productUrl={item.productUrl}
+													onRemove={() => removeItem.mutate(item.id)}
+												/>
+												<div className="px-4 pb-3 -mt-1">
+													<ClassificationBadge
+														classification={item.classification}
+														onCycle={() =>
+															updateClassification.mutate({
+																itemId: item.id,
+																classification: nextClassification(
+																	item.classification,
+																),
+															})
+														}
+													/>
+												</div>
+											</div>
 										))}
 									</div>
 								</div>