refactor(契约): 展示题号统一叫 problemDisplayId，题单 id 统一叫 problemSetId

前后端同时改，部署前开着的旧页面要刷新一次（题号列会是空的、提交筛选会失效）。

- 挂在非题目对象上的展示题号，原来叫 problem（字符串）或 displayId，统一成
  problemDisplayId：提交列表、流程图列表、统计的 lastFailure / items /
  今日最热题、站内信里的提交、后台题单的题目列表。别处的 problem 都是对象
  或数字 id，这几处是字符串，最容易看错
- 列表筛选的 query 参数 ?problemId= 实际传的是展示题号，改成
  ?problemDisplayId=（提交列表、流程图列表、三个统计接口）
- 契约里 problemsetId / problemSetId、problemset / problemSet 两种拼法并存，
  统一成 problemSetId / problemSet，和 ProblemSet* 类型名、problem-sets
  路径、前端路由参数一致。drizzle 的列键跟表名走，没动
- aiDetail.user（用户名字符串，而契约里别的 user 都是对象）→ username。
  ai_analysis.data 里存的历史快照仍是 user，没有代码读回它
- 后台题单题目表的列是按字符串键 'displayId' 取的，类型检查抓不到，一并改

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

apps/api/src/routes/submission.ts

@@ -627,7 +627,7 @@ submissionRoutes.get("/submissions", optionalAuth, async (c) => {
   ) {
     return success(c, { results: [], total: 0 } satisfies SubmissionList)
   }
-  const displayId = c.req.query("problemId")?.trim()
+  const displayId = c.req.query("problemDisplayId")?.trim()
   const myself = c.req.query("myself") === "1" ? user : null
   // 「只看自己」盖过用户名
   const username = myself ? undefined : c.req.query("username")?.trim()
@@ -673,7 +673,7 @@ submissionRoutes.get("/submissions", optionalAuth, async (c) => {
       ({ submission, problem }) =>
         ({
           id: submission.id,
-          problem: problem.displayId,
+          problemDisplayId: problem.displayId,
           problemTitle: problem.title,
           showLink: user
             ? canViewSubmission(user, submission, problem, null, joinTimes)
@@ -708,7 +708,7 @@ submissionRoutes.get(
     const limit = queryInteger(c.req.query("limit"), 10, { min: 1, max: 250 })
     const offset = queryInteger(c.req.query("offset"), 0, { min: 0 })
     const user = c.get("user")
-    const displayId = c.req.query("problemId")?.trim()
+    const displayId = c.req.query("problemDisplayId")?.trim()
     const myself = c.req.query("myself") === "1" ? user : null
     const username = myself ? undefined : c.req.query("username")?.trim()
     const result = c.req.query("result")
@@ -757,7 +757,7 @@ submissionRoutes.get(
         ({ submission, problem }) =>
           ({
             id: submission.id,
-            problem: problem.displayId,
+            problemDisplayId: problem.displayId,
             problemTitle: problem.title,
             showLink: user
               ? canViewSubmission(user, submission, problem, contest)