Show saved-video counts (not channel counts) in the Saved page sidebar

GET /api/feed/saved-counts aggregates, per category, how many videos have
a completed download (using each video's latest job only, same rule as
the existing ?downloaded=true feed filter). CategoryNav gains an optional
categoryCounts override so Feed/Channels keep showing channel_count while
Saved shows this instead.

Query key ['feed', 'saved-counts'] deliberately nests under 'feed' so
DownloadButton's existing invalidateQueries({queryKey: ['feed']}) on
download/delete refreshes these counts too, with no extra wiring.

1 new backend test (77 total).
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

frontend/src/api/client.ts

@@ -217,3 +217,13 @@ export function getFeed(
   const suffix = qs.toString() ? `?${qs.toString()}` : ''
   return request<{ items: FeedVideoDto[]; next_cursor: string | null }>(`/api/feed${suffix}`)
 }
+
+export interface SavedCounts {
+  all: number
+  uncategorized: number
+  categories: Record<string, number>
+}
+
+export function getSavedCounts() {
+  return request<SavedCounts>('/api/feed/saved-counts')
+}