feat: add normalized public search filters

Add strict public search numeric validation and URL-backed category and price filters to the catalog UI.

apps/web/src/pages/CatalogPage.vue

@@ -7,17 +7,23 @@ import ListingCard from '@/components/molecules/ListingCard.vue';
 
 const route = useRoute();
 const router = useRouter();
-const { query, page, result, isLoading, error, load, goToPage } = useCatalogSearch({
+const { query, category, minPriceMinor, maxPriceMinor, page, result, isLoading, error, load, goToPage } = useCatalogSearch({
   initialQuery: typeof route.query.q === 'string' ? route.query.q : '',
+  initialCategory: typeof route.query.category === 'string' ? route.query.category : '',
+  initialMinPriceMinor: Number.parseInt(route.query.min, 10) || undefined,
+  initialMaxPriceMinor: Number.parseInt(route.query.max, 10) || undefined,
   initialPage: Number.parseInt(route.query.page, 10) || 1,
 });
 
 onMounted(load);
 
-watch([query, page], ([nextQuery, nextPage]) => {
+watch([query, category, minPriceMinor, maxPriceMinor, page], ([nextQuery, nextCategory, nextMin, nextMax, nextPage]) => {
   router.replace({
     query: {
       ...(nextQuery ? { q: nextQuery } : {}),
+      ...(nextCategory ? { category: nextCategory } : {}),
+      ...(typeof nextMin === 'number' ? { min: String(nextMin) } : {}),
+      ...(typeof nextMax === 'number' ? { max: String(nextMax) } : {}),
       ...(nextPage > 1 ? { page: String(nextPage) } : {}),
     },
   });
@@ -34,6 +40,11 @@ watch([query, page], ([nextQuery, nextPage]) => {
         <span>Search the catalog</span>
         <input v-model="query" type="search" placeholder="Try Charizard, 151, plush..." />
       </label>
+      <div class="catalog-filters">
+        <label>Category <input v-model="category" type="search" placeholder="Cards or plush" /></label>
+        <label>Min price (cents) <input v-model.number="minPriceMinor" type="number" min="0" /></label>
+        <label>Max price (cents) <input v-model.number="maxPriceMinor" type="number" min="0" /></label>
+      </div>
     </header>
 
     <section class="catalog-results" aria-live="polite">