feat(duplicates): sidebar count + auto-run cross-folder scan

Sidebar Duplicates badge now sums stacks + cross-folder groups, with
cross-folder observed from cache (no eager disk scan from the sidebar).
Cross-folder tab auto-fires the scan on access; button becomes Rescan.

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

web/src/lib/components/layout/LeftSidebar.svelte

@@ -21,13 +21,19 @@
 		logout,
 		renameFolder,
 		renameHeap,
+		scanCrossFolderDuplicates,
 		triggerDownload,
+		type CrossFolderScanResult,
 		type ImportInfo,
 		type PhotoMarksMap,
 		type PpAlbum,
 		type PpClientConfig,
 		type PpFolder
 	} from '$lib/services/photoprism';
+	import {
+		listDuplicateGroups,
+		type DuplicateGroup
+	} from '$lib/services/adapters/duplicates';
 	import {
 		filters,
 		setFolderPath,
@@ -101,6 +107,25 @@
 		staleTime: 60_000
 	}));
 
+	// Duplicates counts for the sidebar badge. Stacks is a cheap
+	// PhotoPrism query so we always fetch it; cross-folder is an
+	// O(disk) scan, so the sidebar only *observes* its cache
+	// (enabled:false) and the duplicates page itself is what populates
+	// it on first visit. Both share queryKeys with the /duplicates
+	// view so cache is reused.
+	const stacksQuery = createQuery<DuplicateGroup[]>(() => ({
+		queryKey: ['duplicates'],
+		queryFn: listDuplicateGroups,
+		enabled: isAuthenticated(),
+		staleTime: 60_000
+	}));
+	const crossFolderQuery = createQuery<CrossFolderScanResult>(() => ({
+		queryKey: ['duplicates-cross-folder'],
+		queryFn: scanCrossFolderDuplicates,
+		enabled: false,
+		staleTime: 5 * 60_000
+	}));
+
 	const ratingsCount = $derived(countRatings(marksQuery.data));
 	const colorsCount = $derived(countColors(marksQuery.data));
 
@@ -365,7 +390,9 @@
 	// "everything visible in the main timeline" tally), so it matches what
 	// the All photos view actually renders. `places` is the count of
 	// geocoded locations — semantically what the Map view groups by.
-	// Duplicates has no precomputed counter; we omit its badge.
+	// Duplicates sums stacks + cross-folder groups; cross-folder only
+	// contributes once its tab has been visited (the scan is opt-in
+	// per-visit, not eager from the sidebar).
 	type ViewItem =
 		| { kind: 'section'; id: Section; label: string; getCount: () => number | undefined }
 		| { kind: 'route'; href: string; label: string; getCount: () => number | undefined };
@@ -395,7 +422,16 @@
 
 	const manageViews: ViewItem[] = [
 		{ kind: 'route', href: '/review', label: 'Review', getCount: () => configQuery.data?.count?.review },
-		{ kind: 'route', href: '/duplicates', label: 'Duplicates', getCount: () => undefined },
+		{
+			kind: 'route',
+			href: '/duplicates',
+			label: 'Duplicates',
+			getCount: () => {
+				const stacks = stacksQuery.data?.length;
+				if (stacks === undefined) return undefined;
+				return stacks + (crossFolderQuery.data?.groups.length ?? 0);
+			}
+		},
 		{ kind: 'section', id: 'hidden', label: 'Hidden', getCount: () => configQuery.data?.count?.hidden },
 		{ kind: 'section', id: 'archive', label: 'Archive', getCount: () => configQuery.data?.count?.archived }
 	];