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>

src/web/api/player.ts

@@ -255,15 +255,17 @@ export function createPlayerRouter(
       // ones, otherwise the playback retry loop wastes time guessing.
       let queueable: { id: string }[] = songs;
       const totalCount = songs.length;
-      const qqLike = provider as { getPlayableSongIds?: (ids: string[]) => Promise<Set<string>> };
+      const qqLike = provider as { getPlayableSongIds?: (ids: string[]) => Promise<Set<string> | null> };
       if (typeof qqLike.getPlayableSongIds === "function") {
         const playable = await qqLike.getPlayableSongIds(songs.map((s: { id: string }) => s.id));
-        if (playable.size > 0) {
+        if (playable !== null) {
+          // Authoritative answer from upstream — even an empty set means
+          // "we know none are playable", short-circuit immediately rather
+          // than wasting 20+ retries.
           queueable = songs.filter((s: { id: string }) => playable.has(s.id));
         }
-        // If batch returned nothing, leave queueable as-is and let the
-        // sequential retry path try anyway (handles the case where the
-        // batch endpoint failed entirely).
+        // If null, the batch endpoint itself errored — fall through to
+        // the sequential retry path, which still has a chance.
       }
       if (queueable.length === 0) {
         res.json({ message: `Loaded ${totalCount} songs but none were playable (likely copyright/region restrictions).` });