R6-E2: return empty collections when user has no school

- _require_institute returns Optional[str] instead of raising 400
- list_classes / my_teaching_classes / my_student_classes / list_school_students
  now return empty arrays when school_id is missing

routers/database/tools/classes_router.py

@@ -31,12 +31,9 @@ def _resolve_institute_id(user_id: str) -> Optional[str]:
         return None
 
 
-def _require_institute(user_id: str) -> str:
+def _require_institute(user_id: str) -> Optional[str]:
-    """Return institute_id or raise 400."""
+    """Return institute_id, or None if the user has no school membership."""
-    institute_id = _resolve_institute_id(user_id)
+    return _resolve_institute_id(user_id)
-    if not institute_id:
-        raise HTTPException(status_code=400, detail="User is not linked to a school")
-    return institute_id
 
 
 def _is_school_admin(user_id: str, institute_id: str) -> bool:
@@ -105,6 +102,8 @@ async def list_classes(
 ) -> Dict[str, Any]:
     user_id = credentials.get("sub", "")
     institute_id = _require_institute(user_id)
+    if not institute_id:
+        return {"classes": [], "total": 0}
     sb = _sb()
 
     q = sb.supabase.table("classes").select("*", count="exact").eq("institute_id", institute_id)
@@ -169,6 +168,8 @@ async def my_teaching_classes(
 ) -> Dict[str, Any]:
     user_id = credentials.get("sub", "")
     institute_id = _require_institute(user_id)
+    if not institute_id:
+        return {"classes": []}
     sb = _sb()
 
     assigned = (
@@ -204,6 +205,8 @@ async def my_student_classes(
 ) -> Dict[str, Any]:
     user_id = credentials.get("sub", "")
     institute_id = _require_institute(user_id)
+    if not institute_id:
+        return {"classes": []}
     sb = _sb()
 
     enrolled = (
@@ -237,6 +240,8 @@ async def list_school_students(
     """List all students in the caller's school. Used by admin to add students to a class."""
     user_id = credentials.get("sub", "")
     institute_id = _require_institute(user_id)
+    if not institute_id:
+        return {"students": []}
     sb = _sb()
     members = (
         sb.supabase.table("institute_memberships")