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>

studio-v2/app/companion/page.tsx

@@ -0,0 +1,51 @@
+'use client'
+
+import { useTheme } from '@/lib/ThemeContext'
+import { Sidebar } from '@/components/Sidebar'
+import { CompanionDashboard } from '@/components/companion/CompanionDashboard'
+import { ThemeToggle } from '@/components/ThemeToggle'
+import { LanguageDropdown } from '@/components/LanguageDropdown'
+
+export default function CompanionPage() {
+  const { isDark } = useTheme()
+
+  return (
+    <div className={`min-h-screen flex relative overflow-hidden ${
+      isDark
+        ? 'bg-gradient-to-br from-indigo-900 via-purple-900 to-pink-800'
+        : 'bg-gradient-to-br from-slate-100 via-blue-50 to-indigo-100'
+    }`}>
+      {/* Animated Background Blobs */}
+      <div className={`absolute -top-40 -right-40 w-96 h-96 rounded-full mix-blend-multiply filter blur-3xl animate-blob ${
+        isDark ? 'bg-purple-500 opacity-30' : 'bg-purple-300 opacity-40'
+      }`} />
+      <div className={`absolute top-1/2 -left-40 w-96 h-96 rounded-full mix-blend-multiply filter blur-3xl animate-blob animation-delay-2000 ${
+        isDark ? 'bg-pink-500 opacity-30' : 'bg-pink-300 opacity-40'
+      }`} />
+
+      {/* Sidebar */}
+      <div className="relative z-10 p-4">
+        <Sidebar />
+      </div>
+
+      {/* Main Content */}
+      <div className="flex-1 flex flex-col relative z-10 p-4 overflow-hidden">
+        {/* Header */}
+        <div className="flex items-center justify-between mb-4">
+          <h1 className={`text-2xl font-bold ${isDark ? 'text-white' : 'text-slate-900'}`}>
+            Companion
+          </h1>
+          <div className="flex items-center gap-2">
+            <ThemeToggle />
+            <LanguageDropdown />
+          </div>
+        </div>
+
+        {/* Companion Dashboard */}
+        <div className="flex-1 overflow-auto">
+          <CompanionDashboard />
+        </div>
+      </div>
+    </div>
+  )
+}