[split-required] Split 700-870 LOC files across all services

backend-lehrer (11 files):
- llm_gateway/routes/schools.py (867 → 5), recording_api.py (848 → 6)
- messenger_api.py (840 → 5), print_generator.py (824 → 5)
- unit_analytics_api.py (751 → 5), classroom/routes/context.py (726 → 4)
- llm_gateway/routes/edu_search_seeds.py (710 → 4)

klausur-service (12 files):
- ocr_labeling_api.py (845 → 4), metrics_db.py (833 → 4)
- legal_corpus_api.py (790 → 4), page_crop.py (758 → 3)
- mail/ai_service.py (747 → 4), github_crawler.py (767 → 3)
- trocr_service.py (730 → 4), full_compliance_pipeline.py (723 → 4)
- dsfa_rag_api.py (715 → 4), ocr_pipeline_auto.py (705 → 4)

website (6 pages):
- audit-checklist (867 → 8), content (806 → 6)
- screen-flow (790 → 4), scraper (789 → 5)
- zeugnisse (776 → 5), modules (745 → 4)

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

backend-lehrer/llm_gateway/routes/schools_db.py

@@ -0,0 +1,25 @@
+"""
+Schools API - Database Connection.
+
+Shared database pool for school endpoints.
+"""
+
+import os
+from typing import Optional
+
+import asyncpg
+
+# Database connection pool
+_pool: Optional[asyncpg.Pool] = None
+
+
+async def get_db_pool() -> asyncpg.Pool:
+    """Get or create database connection pool."""
+    global _pool
+    if _pool is None:
+        database_url = os.environ.get(
+            "DATABASE_URL",
+            "postgresql://breakpilot:breakpilot123@postgres:5432/breakpilot_db"
+        )
+        _pool = await asyncpg.create_pool(database_url, min_size=2, max_size=10)
+    return _pool