refactor: 一批名不副实的命名改掉（只动一端，不碰契约）

后端：
- getUserByToken → authenticateToken：它会删会话、续 TTL、记在线，不是纯读
- todayStart → dayStart(instant)：本来就接受任意时刻，不只是「今天」
- objectValue → asRecord，删掉 4 份一模一样的私有拷贝和 `as toObject` 别名
- 报错文案 "does not exists" / "Already be a public problem" 改通顺

前端：
- utils/types 里 Contest / User / Problem 三个别名删掉：Contest 原来指后台
  比赛、契约里同名的却是学生侧。现在 Contest = 学生侧、AdminContest = 后台，
  后台用户表单叫 AdminUserForm，题目详情直接用 ProblemDetail
- SubmissionInfo → ContestSubmissionInfo，免得和 submission.info 撞名
- utoa / atou → compressToBase64 / decompressFromBase64（实际是 zlib + base64），
  encode / decode → base64EncodeUtf8 / base64DecodeUtf8
- filterResult → toProblemRow、toProblemListItem → toAdminProblemRow，
  行字段 submission / rate → submissionCount / acRate
- 组件：Modal → AddFromLibraryModal、Form → EditorToolbar、
  ContestEditor → BasicEditor（题单也在用它）、rank 的 Index → RankMedal、
  Name → UserNameCell、Password → PasswordCell、ContestType → ContestAccessTag

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

apps/api/src/scripts/recount.ts

@@ -2,7 +2,7 @@ import { eq, sql } from "drizzle-orm"
 
 import { db, schema } from "../db"
 import { JudgeStatus, isAccepted } from "../judge/status"
-import { objectValue } from "../routes/helpers"
+import { asRecord } from "../routes/helpers"
 import {
   metaAchievements,
   refreshUnlockedCount,
@@ -305,7 +305,7 @@ async function computePlan(): Promise<Plan> {
       })
     }
     if (
-      stable(objectValue(problem.statisticInfo)) !== stable(want.statisticInfo)
+      stable(asRecord(problem.statisticInfo)) !== stable(want.statisticInfo)
     ) {
       rows.push({
         label,
@@ -328,7 +328,7 @@ async function computePlan(): Promise<Plan> {
     }
     // acm_problems_status 里除了 problems / contest_problems 之外的键原样保留 ——
     // persistResult 只写这两个桶，别的键是从哪来的没人说得清，重算不该顺手抹掉。
-    const existing = objectValue(profile.acmProblemsStatus)
+    const existing = asRecord(profile.acmProblemsStatus)
     const merged: Record<string, unknown> = { ...existing }
     delete merged.problems
     delete merged.contest_problems
@@ -355,13 +355,13 @@ async function computePlan(): Promise<Plan> {
     }
     if (stable(existing) !== stable(merged)) {
       const keys = new Set([
-        ...Object.keys(objectValue(existing.problems)),
+        ...Object.keys(asRecord(existing.problems)),
         ...Object.keys(want.status.problems ?? {}),
       ])
       rows.push({
         label,
         field: "acm_problems_status",
-        before: `${Object.keys(objectValue(existing.problems)).length} 题`,
+        before: `${Object.keys(asRecord(existing.problems)).length} 题`,
         after: `${keys.size} 题（含比赛桶重建）`,
       })
     }