Fix: asyncpg needs postgresql:// not postgresql+asyncpg://

Strip SQLAlchemy dialect prefix from DATABASE_URL for asyncpg.
Set search_path via server_settings on pool creation.

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

backend-lehrer/vocabulary_db.py

@@ -15,10 +15,15 @@ from typing import Any, Dict, List, Optional
 
 logger = logging.getLogger(__name__)
 
-DATABASE_URL = os.getenv(
+_RAW_DB_URL = os.getenv(
     "DATABASE_URL",
     "postgresql://breakpilot:breakpilot@postgres:5432/breakpilot",
 )
+# Strip SQLAlchemy dialect prefix (asyncpg needs plain postgresql://)
+DATABASE_URL = _RAW_DB_URL.replace("postgresql+asyncpg://", "postgresql://")
+# Strip search_path options (set via SET after connect)
+if "options=" in DATABASE_URL:
+    DATABASE_URL = DATABASE_URL.split("?")[0] if "options=" in DATABASE_URL.split("?")[-1] else DATABASE_URL
 
 _pool = None
 
@@ -28,7 +33,10 @@ async def get_pool():
     global _pool
     if _pool is None:
         import asyncpg
-        _pool = await asyncpg.create_pool(DATABASE_URL, min_size=2, max_size=10)
+        _pool = await asyncpg.create_pool(
+            DATABASE_URL, min_size=2, max_size=10,
+            server_settings={"search_path": "lehrer,core,public"},
+        )
     return _pool