fix: resolve tsc-b build errors (Tex JSX type, Essay index sig, ExamRunner closure, vitest config)

frontend/src/components/ExamRunner.tsx

@@ -59,7 +59,8 @@ export default function ExamRunner({ exam, state, setState, onSubmit, onExit }:
       if (e.key === 'f') toggleFlag()
       if (/^[1-9]$/.test(e.key) && q.type === 'multiple-choice' && q.choices) {
         const ci = parseInt(e.key, 10) - 1
-        if (q.choices[ci]) setState((s) => ({ ...s, answers: { ...s.answers, [q.id]: q.choices[ci].id } }))
+        const choices = q.choices
+        if (choices[ci]) setState((s) => ({ ...s, answers: { ...s.answers, [q.id]: choices[ci].id } }))
       }
     }
     window.addEventListener('keydown', handler)

frontend/src/components/Tex.tsx

@@ -1,14 +1,16 @@
+import type React from 'react'
 import { renderLatex } from '../utils/latex'
 
 interface TexProps {
   children?: string | null
-  tag?: keyof JSX.IntrinsicElements
+  tag?: keyof React.JSX.IntrinsicElements
   className?: string
   style?: React.CSSProperties
 }
 
 // Safe: renderLatex only produces KaTeX-controlled HTML + HTML-escaped plain text.
-export default function Tex({ children, tag: Tag = 'span', className, style }: TexProps) {
+export default function Tex({ children, tag = 'span', className, style }: Readonly<TexProps>) {
+  const Tag = tag as React.ElementType
   const html = String(children ?? '').split('\n').map(renderLatex).join('<br/>')
   return <Tag className={className} style={style} dangerouslySetInnerHTML={{ __html: html }} />
 }

frontend/src/components/questions/Essay.tsx

@@ -3,6 +3,7 @@ import type { Question } from '../../types'
 interface EssayValue {
   text?: string
   selfGrade?: number
+  [key: string]: unknown
 }
 
 interface Props {