diff --git a/src/mcp/server/streamable_http.py b/src/mcp/server/streamable_http.py
index 23ca43b4..53fff0d3 100644
--- a/src/mcp/server/streamable_http.py
+++ b/src/mcp/server/streamable_http.py
@@ -24,7 +24,7 @@
 from starlette.responses import Response
 from starlette.types import Receive, Scope, Send
 
-from mcp.shared.message import SessionMessage
+from mcp.shared.message import ServerMessageMetadata, SessionMessage
 from mcp.types import (
     INTERNAL_ERROR,
     INVALID_PARAMS,
@@ -520,7 +520,7 @@ async def sse_writer():
             )
             await response(scope, receive, send)
             if writer:
-                await writer.send(err)
+                await writer.send(Exception(err))
             return
 
     async def _handle_get_request(self, request: Request, send: Send) -> None:
@@ -834,12 +834,17 @@ async def message_router():
                         ):
                             # Extract related_request_id from meta if it exists
                             if (
-                                (params := getattr(message.root, "params", None))
-                                and (meta := params.get("_meta"))
-                                and (related_id := meta.get("related_request_id"))
+                                session_message.metadata is not None
+                                and isinstance(
+                                    session_message.metadata,
+                                    ServerMessageMetadata,
+                                )
+                                and session_message.metadata.related_request_id
                                 is not None
                             ):
-                                target_request_id = str(related_id)
+                                target_request_id = str(
+                                    session_message.metadata.related_request_id
+                                )
                         else:
                             target_request_id = str(message.root.id)
 
diff --git a/src/mcp/shared/session.py b/src/mcp/shared/session.py
index cbf47be5..d74c4d06 100644
--- a/src/mcp/shared/session.py
+++ b/src/mcp/shared/session.py
@@ -12,7 +12,7 @@
 from typing_extensions import Self
 
 from mcp.shared.exceptions import McpError
-from mcp.shared.message import SessionMessage
+from mcp.shared.message import ServerMessageMetadata, SessionMessage
 from mcp.types import (
     CancelledNotification,
     ClientNotification,
@@ -24,7 +24,6 @@
     JSONRPCNotification,
     JSONRPCRequest,
     JSONRPCResponse,
-    NotificationParams,
     RequestParams,
     ServerNotification,
     ServerRequest,
@@ -288,22 +287,16 @@ async def send_notification(
         """
         # Some transport implementations may need to set the related_request_id
         # to attribute to the notifications to the request that triggered them.
-        if related_request_id is not None and notification.root.params is not None:
-            # Create meta if it doesn't exist
-            if notification.root.params.meta is None:
-                meta_dict = {"related_request_id": related_request_id}
-
-            else:
-                meta_dict = notification.root.params.meta.model_dump(
-                    by_alias=True, mode="json", exclude_none=True
-                )
-                meta_dict["related_request_id"] = related_request_id
-            notification.root.params.meta = NotificationParams.Meta(**meta_dict)
         jsonrpc_notification = JSONRPCNotification(
             jsonrpc="2.0",
             **notification.model_dump(by_alias=True, mode="json", exclude_none=True),
         )
-        session_message = SessionMessage(message=JSONRPCMessage(jsonrpc_notification))
+        session_message = SessionMessage(
+            message=JSONRPCMessage(jsonrpc_notification),
+            metadata=ServerMessageMetadata(related_request_id=related_request_id)
+            if related_request_id
+            else None,
+        )
         await self._write_stream.send(session_message)
 
     async def _send_response(
diff --git a/tests/client/test_logging_callback.py b/tests/client/test_logging_callback.py
index 588fa649..0c9eeb39 100644
--- a/tests/client/test_logging_callback.py
+++ b/tests/client/test_logging_callback.py
@@ -9,7 +9,6 @@
 from mcp.shared.session import RequestResponder
 from mcp.types import (
     LoggingMessageNotificationParams,
-    NotificationParams,
     TextContent,
 )
 
@@ -80,10 +79,7 @@ async def message_handler(
         assert log_result.isError is False
         assert len(logging_collector.log_messages) == 1
         # Create meta object with related_request_id added dynamically
-        meta = NotificationParams.Meta()
-        setattr(meta, "related_request_id", "2")
         log = logging_collector.log_messages[0]
         assert log.level == "info"
         assert log.logger == "test_logger"
         assert log.data == "Test log message"
-        assert log.meta == meta