WebSocket turns carry only new input, so conversation-level plugins see less of a Codex session #1515

Follow-up to #1467, which carries Codex's Responses API WebSocket and parses each turn on it.

The limitation

Over HTTPS, every Codex turn is a POST whose body carries the whole conversation. Over the WebSocket, only the first turn on a socket does. Every later turn carries only the new input items, plus a previous_response_id naming the turn before. The server keeps the earlier context. That is part of why Codex prefers the socket.

#1467 parses each turn exactly as its body reads, so on a socket's later turns Extensions.Inference.Messages holds only the delta, not the conversation.

Who it affects

• Unaffected: inference-parser's model, tokens, cost and tool calls (these come from the response), and tool-prune (each turn carries its own tool list).
• Affected: any plugin that judges the conversation as a whole, for example ibac reading the user's intent across turns, context-guru, or a policy (opa, cpex) written against input.inference.messages. Over the socket such a plugin sees less than it would over HTTPS for the same session.

Codex runs on laptop installs today, where none of those are in the default pipeline. So nothing is broken for current users, but a deployment that enables them for Codex would get weaker coverage without any sign of it.

Possible fixes

1. Rebuild the conversation per socket. The relay already sees every turn's input and every response's output items. It could keep a running transcript per socket and present plugins the full message list, as an HTTPS body would carry. Cost: memory per open socket, and reproducing what the server reconstructs from previous_response_id.
2. Flag the turn as incremental (for example, an Incremental field on InferenceExtension), so a conversation-level plugin can tell it is seeing a delta and decide for itself.
3. Fall back for those pipelines. When the chain contains a plugin that needs the whole conversation, decline the socket (listener.responses_websockets: decline), so Codex uses HTTPS. That is available today as a manual setting.

Refs #1467, #1365.

Assisted-By: Claude (Anthropic AI) noreply@anthropic.com