build: 恢复前端类型检查

vue-tsc 不支持 TypeScript 7，前端单独用 TS 5.9 + vue-tsc（服务端仍是 TS 7），
根目录 bun run typecheck 同时检查两边。修掉前端原有的 8 个类型错误（未使用的变量、类型标注）。

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

client/package.json

@@ -7,7 +7,8 @@
     "dev": "bun --bun vite",
     "build": "bun --bun vite build",
     "build:staging": "bun --bun vite build --mode staging",
-    "fmt": "bun fmt src/"
+    "fmt": "bun fmt src/",
+    "typecheck": "vue-tsc --noEmit -p tsconfig.app.json"
   },
   "dependencies": {
     "@codemirror/lang-css": "^6.3.1",
@@ -36,8 +37,9 @@
     "@vitejs/plugin-vue": "^6.0.10",
     "@vue/tsconfig": "^0.9.1",
     "prettier": "^3.9.10",
-    "typescript": "^7.0.2",
+    "typescript": "~5.9.3",
     "unplugin-vue-components": "^32.1.0",
-    "vite": "^8.3.5"
+    "vite": "^8.3.5",
+    "vue-tsc": "^3.3.13"
   }
 }