feat: colored count badge on Colors sidebar entry

Adds a `colored` field to /library/stats counting non-discarded
photos with a color_label set, mirroring how `rated` is exposed.
The Colors sidebar entry now shows the live count and refreshes
through the existing LIBRARY_STATS_QUERY_KEY invalidations.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

backend/app/routers/library.py

@@ -36,6 +36,8 @@ async def get_library_stats(db: AsyncSession = Depends(get_db)):
       - all_photos:   non-discarded photos + videos (matches the All
                       Photos section's default filter)
       - rated:        non-discarded with rating >= 1
+      - colored:      non-discarded with a color_label set (matches the
+                      Colors grouped view's labeled buckets)
       - duplicates:   non-discarded with is_duplicate = true
       - discarded:    is_discarded = true
       - total_size:   raw bytes across every row, including discarded
@@ -52,6 +54,14 @@ async def get_library_stats(db: AsyncSession = Depends(get_db)):
         )
     ).scalar() or 0
 
+    colored_count = (
+        await db.execute(
+            select(func.count(Photo.id)).where(
+                not_discarded, Photo.color_label.is_not(None)
+            )
+        )
+    ).scalar() or 0
+
     duplicates_count = (
         await db.execute(
             select(func.count(Photo.id)).where(
@@ -85,6 +95,7 @@ async def get_library_stats(db: AsyncSession = Depends(get_db)):
     return {
         "all_photos": all_photos_count,
         "rated": rated_count,
+        "colored": colored_count,
         "duplicates": duplicates_count,
         "discarded": discarded_count,
         "total_photos": photo_count,

frontend/src/components/layout/LeftSidebar.tsx

@@ -348,7 +348,7 @@ export function LeftSidebar({ onCollapse, onOpenSettings }: LeftSidebarProps) {
         { id: 'all-photos', label: 'All Photos', icon: <Image className="h-4 w-4" />, count: stats?.all_photos ?? 0 },
         { id: 'rated', label: 'Rated', icon: <Star className="h-4 w-4" />, count: stats?.rated ?? 0 },
         { id: 'tags', label: 'Tags', icon: <TagIcon className="h-4 w-4" />, count: tagsTotalCount },
-        { id: 'colors', label: 'Colors', icon: <Palette className="h-4 w-4" /> },
+        { id: 'colors', label: 'Colors', icon: <Palette className="h-4 w-4" />, count: stats?.colored ?? 0 },
         { id: 'duplicates', label: 'Duplicates', icon: <Copy className="h-4 w-4" />, count: stats?.duplicates ?? 0 },
         { id: 'discarded', label: 'Discarded', icon: <Trash2 className="h-4 w-4" />, count: stats?.discarded ?? 0 },
       ],

frontend/src/services/api.ts

@@ -409,6 +409,7 @@ export interface DuplicateGroupsResponse {
 export interface LibraryStats {
   all_photos: number
   rated: number
+  colored: number
   duplicates: number
   discarded: number
   total_photos: number