[codex] Send request-scoped turn state over WebSocket

[aibrahim-oai]

Context

Turn state is scoped to one logical turn, but the WebSocket path currently exchanges it through upgrade headers, which are scoped to the physical connection. A connection may be reused across turns, so its handshake cannot represent the turn lifecycle reliably.

Change

Exchange turn state on each WebSocket response request instead:

• send an established value in response.create.client_metadata
• read the returned value from the existing response.metadata event
• retain the first value in the turn-scoped ModelClientSession OnceLock
• start the next logical turn without state, even when it reuses the same WebSocket connection

This gives WebSocket requests the same first-value-wins contract as the existing HTTP path.

Test plan

Integration coverage verifies that:

• WebSocket replays returned state on same-turn follow-ups
• later response metadata does not replace the first value
• state resets at the logical turn boundary without requiring a reconnect

CI validates the full change.

Stack

This is 1/2. #28002 builds on this request-scoped transport to carry established state through compact requests.

[aibrahim-oai]

@codex review

[chatgpt-codex-connector]

💡 Codex Review

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Reviewed commit: 8923c8c496

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[aibrahim-oai]

Stack continues in #28002. @codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Keep them coming!

Reviewed commit: 03b5d176bd

ℹ️ About Codex in GitHub

Your team has set up Codex to review pull requests in this repo. Reviews are triggered when you

• Open a pull request for review
• Mark a draft as ready
• Comment "@codex review".

If Codex has suggestions, it will comment; otherwise it will react with 👍.

Codex can also answer questions or update the PR. Try commenting "@codex address that feedback".

[aibrahim-oai]

Pruned unrelated HTTP-only coverage; this PR now tests only the WebSocket behavior it changes. @codex review