feat(companion): Migrate Companion from admin-v2 to studio-v2 as pure lesson tool

Remove Companion module entirely from admin-v2. Rebuild in studio-v2 as a
focused lesson timer (no dashboard mode). Direct flow: start → active → ended.
Fix timer bug where lastTickRef reset prevented countdown. Add companion link
to Sidebar and i18n translations.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

admin-v2/components/companion/lesson-mode/LessonContainer.tsx

@@ -1,80 +0,0 @@
-'use client'
-
-import { LessonSession, LessonStatus } from '@/lib/companion/types'
-import { LessonStartForm } from './LessonStartForm'
-import { LessonActiveView } from './LessonActiveView'
-import { LessonEndedView } from './LessonEndedView'
-
-interface LessonContainerProps {
-  session: LessonSession | null
-  onStartLesson: (data: { classId: string; subject: string; topic?: string; templateId?: string }) => void
-  onEndLesson: () => void
-  onPauseToggle: () => void
-  onExtendTime: (minutes: number) => void
-  onSkipPhase: () => void
-  onSaveReflection: (rating: number, notes: string, nextSteps: string) => void
-  onAddHomework: (title: string, dueDate: string) => void
-  onRemoveHomework: (id: string) => void
-  loading?: boolean
-}
-
-export function LessonContainer({
-  session,
-  onStartLesson,
-  onEndLesson,
-  onPauseToggle,
-  onExtendTime,
-  onSkipPhase,
-  onSaveReflection,
-  onAddHomework,
-  onRemoveHomework,
-  loading,
-}: LessonContainerProps) {
-  // Determine which view to show based on session state
-  const getView = (): 'start' | 'active' | 'ended' => {
-    if (!session) return 'start'
-
-    const status = session.status
-    if (status === 'completed') return 'ended'
-    if (status === 'not_started') return 'start'
-
-    return 'active'
-  }
-
-  const view = getView()
-
-  if (view === 'start') {
-    return (
-      <LessonStartForm
-        onStart={onStartLesson}
-        loading={loading}
-      />
-    )
-  }
-
-  if (view === 'ended' && session) {
-    return (
-      <LessonEndedView
-        session={session}
-        onSaveReflection={onSaveReflection}
-        onAddHomework={onAddHomework}
-        onRemoveHomework={onRemoveHomework}
-        onStartNew={() => onEndLesson()} // This will clear the session and show start form
-      />
-    )
-  }
-
-  if (session) {
-    return (
-      <LessonActiveView
-        session={session}
-        onPauseToggle={onPauseToggle}
-        onExtendTime={onExtendTime}
-        onSkipPhase={onSkipPhase}
-        onEndLesson={onEndLesson}
-      />
-    )
-  }
-
-  return null
-}