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/ModeToggle.tsx

@@ -1,61 +0,0 @@
-'use client'
-
-import { GraduationCap, Timer, Layout } from 'lucide-react'
-import { CompanionMode } from '@/lib/companion/types'
-
-interface ModeToggleProps {
-  currentMode: CompanionMode
-  onModeChange: (mode: CompanionMode) => void
-  disabled?: boolean
-}
-
-const modes: { id: CompanionMode; label: string; icon: React.ReactNode; description: string }[] = [
-  {
-    id: 'companion',
-    label: 'Companion',
-    icon: <GraduationCap className="w-4 h-4" />,
-    description: 'Dashboard mit Vorschlaegen',
-  },
-  {
-    id: 'lesson',
-    label: 'Lesson',
-    icon: <Timer className="w-4 h-4" />,
-    description: 'Timer und Phasen',
-  },
-  {
-    id: 'classic',
-    label: 'Classic',
-    icon: <Layout className="w-4 h-4" />,
-    description: 'Klassische Ansicht',
-  },
-]
-
-export function ModeToggle({ currentMode, onModeChange, disabled }: ModeToggleProps) {
-  return (
-    <div className="bg-white border border-slate-200 rounded-xl p-1 inline-flex gap-1">
-      {modes.map((mode) => {
-        const isActive = currentMode === mode.id
-        return (
-          <button
-            key={mode.id}
-            onClick={() => onModeChange(mode.id)}
-            disabled={disabled}
-            className={`
-              flex items-center gap-2 px-4 py-2 rounded-lg text-sm font-medium
-              transition-all duration-200
-              ${isActive
-                ? 'bg-slate-900 text-white shadow-sm'
-                : 'text-slate-600 hover:bg-slate-100 hover:text-slate-900'
-              }
-              ${disabled ? 'opacity-50 cursor-not-allowed' : 'cursor-pointer'}
-            `}
-            title={mode.description}
-          >
-            {mode.icon}
-            <span>{mode.label}</span>
-          </button>
-        )
-      })}
-    </div>
-  )
-}