karaoke(app): port single-device playlist from partiverse + tests

点歌单本地管理 — 添加/上移/下移/置顶/删除 + 10 秒撤销倒计时 + YouTube 一键
搜，无 room / 无 ws。删掉了 partiverse 那套 yopu 和弦抓取 / LLM 聊天点歌 /
QR 码（依赖后端，对单机无意义）。logic 全 immutable，21 个 vitest 覆盖
边界（首位上移 noop / 末位下移 noop / 缺失 id / 不变性）。

apps/karaoke/frontend/src/logic/playlist.ts

@@ -0,0 +1,49 @@
+// Playlist 不可变操作。所有函数纯，返回新数组。
+
+export interface Song {
+  id: number
+  singer: string
+  title: string
+}
+
+export type Direction = 'up' | 'down' | 'first'
+
+export function nextId(playlist: Song[]): number {
+  let max = 0
+  for (const s of playlist) if (s.id > max) max = s.id
+  return max + 1
+}
+
+export function addSong(playlist: Song[], singer: string, title: string): Song[] {
+  const s = singer.trim()
+  const t = title.trim()
+  if (!s || !t) return playlist
+  return [...playlist, { id: nextId(playlist), singer: s, title: t }]
+}
+
+export function deleteSong(playlist: Song[], songId: number): Song[] {
+  return playlist.filter((s) => s.id !== songId)
+}
+
+export function moveSong(playlist: Song[], songId: number, direction: Direction): Song[] {
+  const idx = playlist.findIndex((s) => s.id === songId)
+  if (idx === -1) return playlist
+  const next = [...playlist]
+  const [song] = next.splice(idx, 1)
+  if (direction === 'first') {
+    next.unshift(song)
+  } else if (direction === 'up') {
+    next.splice(Math.max(0, idx - 1), 0, song)
+  } else {
+    // 'down': insert at idx + 1 of original. After splice, original idx + 1
+    // becomes position idx in `next`. So inserting at idx puts the song before
+    // the element that *was* at idx + 1 — we want *after* it, hence idx + 1.
+    next.splice(Math.min(next.length, idx + 1), 0, song)
+  }
+  return next
+}
+
+export function youtubeSearchUrl(song: Song): string {
+  const q = encodeURIComponent(`${song.singer} ${song.title}`)
+  return `https://www.youtube.com/results?search_query=${q}`
+}

apps/karaoke/frontend/src/logic/storage.ts

@@ -0,0 +1,32 @@
+import type { Song } from './playlist'
+
+interface PersistedState {
+  playlist: Song[]
+}
+
+const KEY = 'karaoke:v1'
+
+function isBrowser(): boolean {
+  return typeof window !== 'undefined' && typeof window.localStorage !== 'undefined'
+}
+
+export function loadState(): PersistedState {
+  if (!isBrowser()) return { playlist: [] }
+  try {
+    const raw = window.localStorage.getItem(KEY)
+    if (!raw) return { playlist: [] }
+    const parsed = JSON.parse(raw) as Partial<PersistedState>
+    return { playlist: parsed.playlist ?? [] }
+  } catch {
+    return { playlist: [] }
+  }
+}
+
+export function saveState(state: PersistedState): void {
+  if (!isBrowser()) return
+  try {
+    window.localStorage.setItem(KEY, JSON.stringify(state))
+  } catch {
+    // ignore
+  }
+}