move functionality to after protocolVersion check

Author: bjoaquinc

src/mcp/client/session.py

@@ -167,12 +167,12 @@ async def initialize(self) -> types.InitializeResult:
             types.InitializeResult,
         )
 
-        if self._client_info is DEFAULT_CLIENT_INFO:
-            self._client_info = result.serverInfo
-
         if result.protocolVersion not in SUPPORTED_PROTOCOL_VERSIONS:
             raise RuntimeError(f"Unsupported protocol version from the server: {result.protocolVersion}")
 
+        if self._client_info is DEFAULT_CLIENT_INFO:
+            self._client_info = result.serverInfo
+
         await self.send_notification(types.ClientNotification(types.InitializedNotification()))
 
         return result