fix: corner-case audit — distinguish failures, recover from blips

Three small but real correctness fixes from auditing recent commits:

1. getPlayableSongIds returned an empty Set for both "endpoint failed"
   and "succeeded but all unplayable" — the caller couldn't tell which.
   Return Set | null now: null = error (fall through to sequential
   retry), empty Set = authoritative "all unplayable" (short-circuit
   to a clear message instead of wasting 20+ retries).

2. Web store: fetchHomeData unconditionally wrote lastFetchTime even
   when every fetch rejected (network blip, server down). That cached
   the failure for 5 minutes — user had to hard-reload to recover.
   Now only commit lastFetchTime if at least one auth-status call
   succeeded.

3. Settings profile section: if GET /profile failed, profileConfigs
   stayed undefined and the row showed "加载中..." forever. Track a
   per-bot error state and render an inline "加载失败 / 重试" link
   so the user can recover without page reload.

Out of scope but documented:
- ein=29 hardcoded in fetchCollectedPlaylists (no pagination yet —
  users with 30+ collected QQ playlists get truncated).
- /play-song single-failure UX (returns "Cannot play" message but
  frontend ignores; needs a global toast/notification primitive).
- NetEase has no analogous batch precheck (could surface same
  "click and wait silent" issue if user has region-restricted NetEase
  playlists).

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

web/src/stores/player.ts

@@ -426,7 +426,15 @@ export const usePlayerStore = defineStore('player', {
         this.bilibiliPopular = bili.value.data.songs ?? [];
       }
 
-      this.lastFetchTime = Date.now();
+      // Only mark as fetched if at least the auth-status calls succeeded —
+      // a fully failed fetch (network blip / server down) should NOT be
+      // cached for 5 minutes, otherwise the user has to hard-reload to
+      // recover when connectivity returns.
+      const authOk =
+        neAuthRes.status === 'fulfilled' || qqAuthRes.status === 'fulfilled';
+      if (authOk) {
+        this.lastFetchTime = Date.now();
+      }
     },
   },
 });