feat(duplicates): show count badges on Stacks/Cross-folder tabs

Stacks count appears immediately (cheap query); cross-folder count fills
in after its tab is visited (lazy disk scan). Page observes both queries
from cache so badges stay in sync with the panel content.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

web/src/routes/duplicates/+page.svelte

@@ -6,6 +6,10 @@
 		listDuplicateGroups,
 		type DuplicateGroup
 	} from '$lib/services/adapters/duplicates';
+	import {
+		scanCrossFolderDuplicates,
+		type CrossFolderScanResult
+	} from '$lib/services/photoprism';
 	import { isAuthenticated } from '$lib/stores/session.svelte';
 	import {
 		setThumbnailSize,
@@ -19,10 +23,6 @@
 	// Same pill-tab pattern as /tags: tab state is URL-driven so the user
 	// can share / refresh / hit Back and land on the right panel.
 	type Tab = 'stacks' | 'cross-folder';
-	const TABS: { id: Tab; label: string }[] = [
-		{ id: 'stacks', label: 'Stacks' },
-		{ id: 'cross-folder', label: 'Cross-folder' }
-	];
 	const activeTab = $derived<Tab>(parseTab(page.url.searchParams.get('tab')));
 	function parseTab(raw: string | null): Tab {
 		return raw === 'cross-folder' ? 'cross-folder' : 'stacks';
@@ -39,12 +39,31 @@
 	// Stale-time matches mule-image's DuplicatesView (30 s) so quick
 	// toolbar bounces don't refetch the (potentially expensive) stack
 	// listing. Invalidation by mutations is explicit, not time-driven.
+	// Enabled on both tabs so the stacks-count badge stays accurate even
+	// while the cross-folder tab is open.
 	const dupesQuery = createQuery<DuplicateGroup[]>(() => ({
 		queryKey: ['duplicates'],
 		queryFn: listDuplicateGroups,
-		enabled: isAuthenticated() && activeTab === 'stacks',
+		enabled: isAuthenticated(),
 		staleTime: 30_000
 	}));
+
+	// Observe-only: DuplicatesView's matching query (same key) is what
+	// actually triggers the scan when the cross-folder tab is active.
+	// Here we just read the cached count for the tab badge.
+	const crossQuery = createQuery<CrossFolderScanResult>(() => ({
+		queryKey: ['duplicates-cross-folder'],
+		queryFn: scanCrossFolderDuplicates,
+		enabled: false,
+		staleTime: 5 * 60_000
+	}));
+
+	const stacksCount = $derived(dupesQuery.data?.length);
+	const crossCount = $derived(crossQuery.data?.groups.length);
+	const TABS = $derived<{ id: Tab; label: string; count: number | undefined }[]>([
+		{ id: 'stacks', label: 'Stacks', count: stacksCount },
+		{ id: 'cross-folder', label: 'Cross-folder', count: crossCount }
+	]);
 </script>
 
 <Toolbar>
@@ -52,17 +71,29 @@
 		Duplicates
 	</span>
 	<!-- Tabs mirror /tags' pill row visually: same height, same active
-	     treatment, same hover affordance. -->
+	     treatment, same hover affordance. Count badge appears once the
+	     underlying query has data — cross-folder stays unbadged until
+	     the tab has been opened at least once (lazy scan). -->
 	<div class="flex items-center gap-1">
 		{#each TABS as t (t.id)}
 			<button
 				type="button"
-				class="rounded border px-2 py-0.5 text-[11px] {activeTab === t.id
+				class="inline-flex items-center gap-1 rounded border px-2 py-0.5 text-[11px] {activeTab === t.id
 					? 'border-primary/40 bg-primary/10 text-primary'
 					: 'border-border text-muted-foreground hover:bg-accent hover:text-foreground'}"
 				onclick={() => setTab(t.id)}
 			>
-				{t.label}
+				<span>{t.label}</span>
+				{#if t.count !== undefined}
+					<span
+						class="flex h-4 min-w-4.5 items-center justify-center rounded px-1 text-[10px] tabular-nums {activeTab ===
+						t.id
+							? 'bg-primary/15 text-primary'
+							: 'bg-secondary text-muted-foreground'}"
+					>
+						{t.count}
+					</span>
+				{/if}
 			</button>
 		{/each}
 	</div>