refactor: fold post_writer signaling closes into async with

Both post_writer tasks (sse, streamable_http) used a try/finally to
close signaling stream ends after the loop. Since the except handlers
only log and don't touch those streams, the closes can move into the
existing async with header — __aexit__ runs before except, which is
fine when the handler doesn't send on the closed stream.

sse_reader can't do the same: its except Exception handler sends on
read_stream_writer (L120), so it must stay open until after the
handler runs.

Author: maxisbey

src/mcp/client/sse.py

@@ -123,7 +123,7 @@ async def sse_reader(task_status: TaskStatus[str] = anyio.TASK_STATUS_IGNORED):
 
             async def post_writer(endpoint_url: str):
                 try:
-                    async with write_stream_reader:
+                    async with write_stream_reader, write_stream:
                         async for session_message in write_stream_reader:
                             logger.debug(f"Sending client message: {session_message}")
                             response = await client.post(
@@ -138,8 +138,6 @@ async def post_writer(endpoint_url: str):
                             logger.debug(f"Client message sent successfully: {response.status_code}")
                 except Exception:  # pragma: lax no cover
                     logger.exception("Error in post_writer")
-                finally:
-                    await write_stream.aclose()
 
             # On Python 3.14, coverage.py reports a phantom branch arc on this
             # line (->yield) when nested two async-with levels deep. The branch

src/mcp/client/streamable_http.py

@@ -440,7 +440,7 @@ async def post_writer(
     ) -> None:
         """Handle writing requests to the server."""
         try:
-            async with write_stream_reader:
+            async with write_stream_reader, read_stream_writer, write_stream:
                 async for session_message in write_stream_reader:
                     message = session_message.message
                     metadata = (
@@ -480,9 +480,6 @@ async def handle_request_async():
 
         except Exception:  # pragma: lax no cover
             logger.exception("Error in post_writer")
-        finally:
-            await read_stream_writer.aclose()
-            await write_stream.aclose()
 
     async def terminate_session(self, client: httpx.AsyncClient) -> None:
         """Terminate the session by sending a DELETE request."""