## Why
Building a Responses WebSocket request copied the model, instructions, input
history, tools, and other request settings into a second payload before
serialization.
## What changed
- Make `ResponseCreateWsRequest` borrow shared fields from
`ResponsesApiRequest`.
- Keep only WebSocket-specific fields owned, and allocate a separate input
vector only for incremental continuations.
- Restore response item IDs after preparing a full request so the request
retained for continuation matching keeps its original state.
## Testing
Update the serialization test to verify that the borrowed WebSocket request
produces the same wire payload as the Responses API request plus its
WebSocket-specific fields.
GitOrigin-RevId: b63d746b7f5164b5204ab95b057c914a4aeb71e1
Charlie Marsh
6b9a5592a6