fix(client): propagate HTTP transport exceptions to caller

ROOT CAUSE:
In SSE and StreamableHTTP transports, when HTTP errors occur or other
exceptions are raised in post_writer, exceptions are caught and logged
but never sent to read_stream_writer, causing the caller to hang
indefinitely waiting for a response that will never arrive.

CHANGES:
- sse.py: Send exceptions from post_writer to read_stream_writer
- streamable_http.py: Send exceptions from post_writer to read_stream_writer

IMPACT:
This prevents callers from hanging when HTTP errors occur in the
transport layer, ensuring exceptions are properly propagated to the
caller for handling.

FILES MODIFIED:
- src/mcp/client/sse.py
- src/mcp/client/streamable_http.py

Reported-by: gspeter
Github-Issue: #2110

Author: peter-luminova

src/mcp/client/sse.py

@@ -144,8 +144,9 @@ async def post_writer(endpoint_url: str):
                                     )
                                     response.raise_for_status()
                                     logger.debug(f"Client message sent successfully: {response.status_code}")
-                        except Exception:  # pragma: lax no cover
+                        except Exception as exc:  # pragma: lax no cover
                             logger.exception("Error in post_writer")
+                            await read_stream_writer.send(exc)
                         finally:
                             await write_stream.aclose()
 

src/mcp/client/streamable_http.py

@@ -478,8 +478,9 @@ async def handle_request_async():
                     else:
                         await handle_request_async()
 
-        except Exception:  # pragma: lax no cover
+        except Exception as exc:  # pragma: lax no cover
             logger.exception("Error in post_writer")
+            await read_stream_writer.send(exc)
         finally:
             await read_stream_writer.aclose()
             await write_stream.aclose()