[split-required] Split 500-1000 LOC files across all services

backend-lehrer (5 files):
- alerts_agent/db/repository.py (992 → 5), abitur_docs_api.py (956 → 3)
- teacher_dashboard_api.py (951 → 3), services/pdf_service.py (916 → 3)
- mail/mail_db.py (987 → 6)

klausur-service (5 files):
- legal_templates_ingestion.py (942 → 3), ocr_pipeline_postprocess.py (929 → 4)
- ocr_pipeline_words.py (876 → 3), ocr_pipeline_ocr_merge.py (616 → 2)
- KorrekturPage.tsx (956 → 6)

website (5 pages):
- mail (985 → 9), edu-search (958 → 8), mac-mini (950 → 7)
- ocr-labeling (946 → 7), audit-workspace (871 → 4)

studio-v2 (5 files + 1 deleted):
- page.tsx (946 → 5), MessagesContext.tsx (925 → 4)
- korrektur (914 → 6), worksheet-cleanup (899 → 6)
- useVocabWorksheet.ts (888 → 3)
- Deleted dead page-original.tsx (934 LOC)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

studio-v2/app/_components/BackgroundBlobs.tsx

@@ -0,0 +1,41 @@
+'use client'
+
+interface BackgroundBlobsProps {
+  isDark: boolean
+}
+
+export function BackgroundBlobs({ isDark }: BackgroundBlobsProps) {
+  return (
+    <>
+      <div className="absolute inset-0 overflow-hidden pointer-events-none">
+        <div className={`absolute -top-40 -right-40 w-80 h-80 rounded-full mix-blend-multiply filter blur-3xl animate-blob ${
+          isDark ? 'bg-purple-500 opacity-70' : 'bg-purple-300 opacity-50'
+        }`} />
+        <div className={`absolute -bottom-40 -left-40 w-80 h-80 rounded-full mix-blend-multiply filter blur-3xl animate-blob animation-delay-2000 ${
+          isDark ? 'bg-blue-500 opacity-70' : 'bg-blue-300 opacity-50'
+        }`} />
+        <div className={`absolute top-1/2 left-1/2 transform -translate-x-1/2 -translate-y-1/2 w-80 h-80 rounded-full mix-blend-multiply filter blur-3xl animate-blob animation-delay-4000 ${
+          isDark ? 'bg-pink-500 opacity-70' : 'bg-pink-300 opacity-50'
+        }`} />
+      </div>
+
+      <style jsx>{`
+        @keyframes blob {
+          0% { transform: translate(0px, 0px) scale(1); }
+          33% { transform: translate(30px, -50px) scale(1.1); }
+          66% { transform: translate(-20px, 20px) scale(0.9); }
+          100% { transform: translate(0px, 0px) scale(1); }
+        }
+        .animate-blob {
+          animation: blob 7s infinite;
+        }
+        .animation-delay-2000 {
+          animation-delay: 2s;
+        }
+        .animation-delay-4000 {
+          animation-delay: 4s;
+        }
+      `}</style>
+    </>
+  )
+}