[codex] Send request-scoped turn state over WebSocket

[aibrahim-oai]

Summary

Carry opaque turn state in each WebSocket response.create request and accept updates from response metadata.

• send state per request rather than in connection upgrade headers
• reuse the latest value across requests in the same turn and on reconnect
• reset state for each new logical turn, even when the WebSocket connection is reused
• preserve updates when compaction crosses between WebSocket and HTTP

Stack

1. [codex] Make turn state replaceable #27930 — replaceable HTTP turn state
2. [codex] Round-trip turn state through compact #27931 — compact round-trip
3. [codex] Send request-scoped turn state over WebSocket #27929 — WebSocket request metadata (this PR)

Coverage

• WebSocket response metadata replaces state within a session
• same-turn follow-ups replay updates while the next turn starts empty
• a model change on a reused connection sends a full create and then accepts replacement state
• WebSocket v2 compact round-trips state on one connection
• WebSocket sampling with v1 HTTP compact carries the update back to WebSocket continuation

[aibrahim-oai]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. What shall we delve into next?

Reviewed commit: e0d264cdc2

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[aibrahim-oai]

Closing this stack to replace it with one consolidated PR.

[aibrahim-oai]

Replaced by #27996.