## 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.
Ahmed Ibrahim
640d61b121