Revert "refactor: reorganize message handling for better type safety and clar…" (#282)

This reverts commit 9d0f2daddb.

src/mcp/server/lowlevel/server.py

@@ -74,6 +74,7 @@ from contextlib import AbstractAsyncContextManager, AsyncExitStack, asynccontext
 from typing import Any, AsyncIterator, Generic, TypeVar
 
 import anyio
+from anyio.streams.memory import MemoryObjectReceiveStream, MemoryObjectSendStream
 from pydantic import AnyUrl
 
 import mcp.types as types
@@ -83,7 +84,7 @@ from mcp.server.session import ServerSession
 from mcp.server.stdio import stdio_server as stdio_server
 from mcp.shared.context import RequestContext
 from mcp.shared.exceptions import McpError
-from mcp.shared.session import ReadStream, RequestResponder, WriteStream
+from mcp.shared.session import RequestResponder
 
 logger = logging.getLogger(__name__)
 
@@ -473,8 +474,8 @@ class Server(Generic[LifespanResultT]):
 
     async def run(
         self,
-        read_stream: ReadStream,
-        write_stream: WriteStream,
+        read_stream: MemoryObjectReceiveStream[types.JSONRPCMessage | Exception],
+        write_stream: MemoryObjectSendStream[types.JSONRPCMessage],
         initialization_options: InitializationOptions,
         # When False, exceptions are returned as messages to the client.
         # When True, exceptions are raised, which will cause the server to shut down