refactor(前端): shared / utils 不再 import oj 和 admin 下的任何东西

依赖方向原来是反的：顶栏、登录框、举手列表这些 shared 组件从 oj/ 里拿东西。
- 跨端的接口挪进 shared/api.ts（按 apps/web/CLAUDE.md 的分法）：学生端题目列表、
  出题人列表、这节课的题、待弹的成就
- 这节课的 store → shared/store/lesson.ts；头像 RankAvatar → shared/components
- 纯函数挪进 utils/：举手列表的错法归类 errorKind、它依赖的答案错误分类 wrongAnswer
  和 Python 报错翻译 pythonError、题目列表行的 toProblemRow
- 只有后台在用的出题人下拉 AuthorSelect 挪回 admin/components

纯搬家。首页、题目列表、题目页、排名、课堂看板、后台题目列表打开无报错，
顶栏题号框敲 1001 回车直达题目页。

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

apps/web/src/shared/api.ts

@@ -1,8 +1,16 @@
 import type { LoginRequest, RegisterRequest } from "@oj2/contract"
-import type { Quote, WebsiteConfig } from "@oj2/contract"
+import type {
+  ClassActivity,
+  MarkAchievementsRead,
+  ProblemAuthor,
+  ProblemList,
+  Quote,
+  WebsiteConfig,
+} from "@oj2/contract"
 import api from "utils/api"
 import { contractDeferred } from "utils/contract"
-import type { Profile, Tag } from "utils/types"
+import { toProblemRow } from "utils/transforms"
+import type { PendingAchievement, Profile, Tag } from "utils/types"
 
 export function login(data: { username: string; password: string }) {
   return api.post("auth/login", data satisfies LoginRequest)
@@ -51,3 +59,35 @@ export function getClassUsernames(classroom: string) {
 export function getWebsiteConfig() {
   return api.get<WebsiteConfig>("site")
 }
+
+export async function getProblemList(
+  offset = 0,
+  limit = 10,
+  searchParams: Record<string, unknown> = {},
+) {
+  const res = await api.get<ProblemList>("problems", {
+    params: { paging: true, offset, limit, ...searchParams },
+  })
+  return {
+    results: res.results.map(toProblemRow),
+    total: res.total,
+  }
+}
+
+export function getAuthors(all = false) {
+  return api.get<ProblemAuthor[]>("problem-authors", {
+    params: { all: all ? "1" : "0" },
+  })
+}
+
+export function getClassActivity() {
+  return api.get<ClassActivity>("me/class-activity")
+}
+
+export function getPendingAchievements() {
+  return api.get<PendingAchievement[]>("achievements/pending")
+}
+
+export function markAchievementsRead(ids: number[]) {
+  return api.post("achievements/pending/read", { ids } satisfies MarkAchievementsRead)
+}