feat(kugou): add login-gated discovery (daily/recommend/user playlists, FM) + covers

Implements the NetEase-parity login features for the Kugou provider now that
QR login works:
- getDailyRecommendSongs (每日推荐), getUserPlaylists (我的歌单), and a real
  getRecommendPlaylists (推荐歌单, was a stub) ported from the reference API.
- mapKugouSong now extracts cover art per endpoint (sizable_cover / cover /
  trans_param.union_cover, resolving the {size} template) — Kugou songs had no
  artwork before.
- Fix the playlist-song shape (combined "歌手 - 歌名" in `name`, mixsongid as the
  audio id) so opened playlists show real titles instead of 未知歌曲.
- New defensive playlist mappers keyed on global_collection_id (the only id
  getPlaylistSongs can open); dedup user playlists in case the list endpoint
  ignores pagination; firstStr() so an empty-string field can't mask a real one.

Frontend wires Kugou as a third home-discovery source (Source type, store
caches/auth, availableSources, fetchHomeData, Home FM card + source tabs,
SourceTabs label, persisted-tab whitelist). SourceTabs now highlights the
fallback-corrected source so the active tab shows when a logged-out source was
persisted (newly possible with 3 sources).

Adds kugou.test.ts coverage for the new mappers, the cover/empty-string and
playlist-shape handling, and id openability.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

web/src/views/Home.vue

@@ -41,13 +41,23 @@
         </div>
         <Icon icon="mdi:play-circle" class="fm-play-icon" />
       </div>
+      <div v-if="store.authStatus.kugou" class="fm-card hover-scale" @click="playFm('kugou')">
+        <div class="fm-icon-wrapper kugou">
+          <Icon icon="mdi:radio-tower" class="fm-icon" />
+        </div>
+        <div class="fm-info">
+          <div class="fm-title">酷狗私人电台</div>
+          <div class="fm-desc">个性化推荐歌曲流</div>
+        </div>
+        <Icon icon="mdi:play-circle" class="fm-play-icon" />
+      </div>
     </section>
 
     <!-- 每日推荐 -->
     <section class="section" v-if="dailyAvailable.length > 0">
       <h2 class="section-title">
         每日推荐
-        <SourceTabs v-model="dailySource" :sources="dailyAvailable" />
+        <SourceTabs :model-value="dailySourceSafe" @update:model-value="dailySource = $event" :sources="dailyAvailable" />
       </h2>
       <div class="daily-grid">
         <div
@@ -67,7 +77,7 @@
     <section class="section" v-if="recommendAvailable.length > 0">
       <h2 class="section-title">
         推荐歌单
-        <SourceTabs v-model="recommendSource" :sources="recommendAvailable" />
+        <SourceTabs :model-value="recommendSourceSafe" @update:model-value="recommendSource = $event" :sources="recommendAvailable" />
       </h2>
       <div class="playlist-grid">
         <RouterLink
@@ -108,7 +118,7 @@
       <h2 class="section-title">
         我的歌单
         <span v-if="currentUserPlaylists.length > 0" class="section-count">{{ currentUserPlaylists.length }}</span>
-        <SourceTabs v-model="userSource" :sources="userAvailable" />
+        <SourceTabs :model-value="userSourceSafe" @update:model-value="userSource = $event" :sources="userAvailable" />
       </h2>
       <div class="playlist-grid">
         <RouterLink
@@ -173,6 +183,7 @@ const userPlaylistsExpanded = ref(false);
 const recommendAvailable = computed<Source[]>(() => {
   const s: Source[] = ['netease'];
   if (store.authStatus.qq) s.push('qq');
+  if (store.authStatus.kugou) s.push('kugou');
   return s;
 });
 const dailyAvailable = computed<Source[]>(() => store.availableSources);
@@ -358,6 +369,10 @@ onMounted(() => {
   &.qq {
     background: linear-gradient(135deg, var(--brand-qq), #17a2b8);
   }
+
+  &.kugou {
+    background: linear-gradient(135deg, var(--brand-kugou), #1d7fd1);
+  }
 }
 
 .fm-icon {