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')
+}

frontend/src/components/CategoryNav.tsx

@@ -8,9 +8,12 @@ interface Props {
   onChange: (filter: CategoryFilter) => void
   allCount?: number
   uncategorizedCount?: number
+  // Overrides each category's displayed count (channel_count by default) --
+  // e.g. the Saved page shows saved-video counts instead.
+  categoryCounts?: Record<number, number>
 }
 
-function CategoryNav({ categories, value, onChange, allCount, uncategorizedCount }: Props) {
+function CategoryNav({ categories, value, onChange, allCount, uncategorizedCount, categoryCounts }: Props) {
   return (
     <nav className="category-nav">
       <button className={value === 'all' ? 'active' : ''} onClick={() => onChange('all')}>
@@ -28,7 +31,9 @@ function CategoryNav({ categories, value, onChange, allCount, uncategorizedCount
           onClick={() => onChange(category.id)}
         >
           {category.name}
-          <span className="category-nav-count">{category.channel_count}</span>
+          <span className="category-nav-count">
+            {categoryCounts ? categoryCounts[category.id] ?? 0 : category.channel_count}
+          </span>
         </button>
       ))}
     </nav>

frontend/src/pages/Saved.tsx

@@ -1,6 +1,6 @@
 import { useInfiniteQuery, useQuery } from '@tanstack/react-query'
 import { Link } from 'react-router-dom'
-import { getFeed, listCategories, listChannels } from '../api/client'
+import { getFeed, getSavedCounts, listCategories } from '../api/client'
 import CategoryNav, { type CategoryFilter } from '../components/CategoryNav'
 import VideoCard from '../components/VideoCard'
 import { useState } from 'react'
@@ -11,12 +11,13 @@ function Saved() {
   const categoriesQuery = useQuery({ queryKey: ['categories'], queryFn: listCategories })
   const categories = categoriesQuery.data ?? []
 
-  const allChannelsQuery = useQuery({
-    queryKey: ['channels', 'all-for-counts'],
-    queryFn: () => listChannels({ subscribed: true }),
-  })
-  const allChannels = allChannelsQuery.data ?? []
-  const uncategorizedCount = allChannels.filter((c) => c.category_ids.length === 0).length
+  // Keyed under 'feed' so DownloadButton's existing invalidateQueries({
+  // queryKey: ['feed'] }) on download/delete also refreshes these counts.
+  const savedCountsQuery = useQuery({ queryKey: ['feed', 'saved-counts'], queryFn: getSavedCounts })
+  const savedCounts = savedCountsQuery.data
+  const categoryCounts = Object.fromEntries(
+    Object.entries(savedCounts?.categories ?? {}).map(([id, count]) => [Number(id), count]),
+  )
 
   const feedQuery = useInfiniteQuery({
     queryKey: ['feed', 'saved', filter],
@@ -49,8 +50,9 @@ function Saved() {
           categories={categories}
           value={filter}
           onChange={setFilter}
-          allCount={allChannels.length}
-          uncategorizedCount={uncategorizedCount}
+          allCount={savedCounts?.all}
+          uncategorizedCount={savedCounts?.uncategorized}
+          categoryCounts={categoryCounts}
         />
 
         <div className="content">