Close unclosed resources in the whole project (#267)

* Close resources

* Close all resources

* Update pyproject.toml

* Close all resources

* Close all resources

* try now...

* try to ignore this

* try again

* try adding one more..

* try now

* try now

* revert ci changes

src/mcp/shared/session.py

@@ -1,4 +1,5 @@
 import logging
+from contextlib import AsyncExitStack
 from datetime import timedelta
 from typing import Any, Callable, Generic, TypeVar
 
@@ -180,6 +181,7 @@ class BaseSession(
         self._read_timeout_seconds = read_timeout_seconds
         self._in_flight = {}
 
+        self._exit_stack = AsyncExitStack()
         self._incoming_message_stream_writer, self._incoming_message_stream_reader = (
             anyio.create_memory_object_stream[
                 RequestResponder[ReceiveRequestT, SendResultT]
@@ -187,6 +189,12 @@ class BaseSession(
                 | Exception
             ]()
         )
+        self._exit_stack.push_async_callback(
+            lambda: self._incoming_message_stream_reader.aclose()
+        )
+        self._exit_stack.push_async_callback(
+            lambda: self._incoming_message_stream_writer.aclose()
+        )
 
     async def __aenter__(self) -> Self:
         self._task_group = anyio.create_task_group()
@@ -195,6 +203,7 @@ class BaseSession(
         return self
 
     async def __aexit__(self, exc_type, exc_val, exc_tb):
+        await self._exit_stack.aclose()
         # Using BaseSession as a context manager should not block on exit (this
         # would be very surprising behavior), so make sure to cancel the tasks
         # in the task group.
@@ -222,6 +231,9 @@ class BaseSession(
         ](1)
         self._response_streams[request_id] = response_stream
 
+        self._exit_stack.push_async_callback(lambda: response_stream.aclose())
+        self._exit_stack.push_async_callback(lambda: response_stream_reader.aclose())
+
         jsonrpc_request = JSONRPCRequest(
             jsonrpc="2.0",
             id=request_id,