Support alternative websocket API (#10861)

**Test plan**

```
cargo build -p codex-cli && RUST_LOG='codex_api::endpoint::responses_websocket=trace,codex_core::client=debug,codex_core::codex=debug' \
  ./target/debug/codex \
    --enable responses_websockets_v2 \
    --profile byok \
    --full-auto
```

codex-rs/codex-api/src/common.rs

@@ -172,6 +172,8 @@ pub struct ResponsesApiRequest<'a> {
 pub struct ResponseCreateWsRequest {
     pub model: String,
     pub instructions: String,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub previous_response_id: Option<String>,
     pub input: Vec<ResponseItem>,
     pub tools: Vec<Value>,
     pub tool_choice: String,