Support custom client info throughout client APIs (#474)

Co-authored-by: Claude <noreply@anthropic.com>

src/mcp/client/__main__.py

@@ -38,9 +38,13 @@ async def message_handler(
 async def run_session(
     read_stream: MemoryObjectReceiveStream[JSONRPCMessage | Exception],
     write_stream: MemoryObjectSendStream[JSONRPCMessage],
+    client_info: types.Implementation | None = None,
 ):
     async with ClientSession(
-        read_stream, write_stream, message_handler=message_handler
+        read_stream,
+        write_stream,
+        message_handler=message_handler,
+        client_info=client_info,
     ) as session:
         logger.info("Initializing session")
         await session.initialize()