Websocket append support (#9128)

Support an incremental append request in websocket transport.

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

@@ -136,6 +136,38 @@ pub struct ResponsesApiRequest<'a> {
     pub text: Option<TextControls>,
 }
 
+#[derive(Debug, Serialize)]
+pub struct ResponseCreateWsRequest {
+    pub model: String,
+    pub instructions: String,
+    pub input: Vec<ResponseItem>,
+    pub tools: Vec<Value>,
+    pub tool_choice: String,
+    pub parallel_tool_calls: bool,
+    pub reasoning: Option<Reasoning>,
+    pub store: bool,
+    pub stream: bool,
+    pub include: Vec<String>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub prompt_cache_key: Option<String>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub text: Option<TextControls>,
+}
+
+#[derive(Debug, Serialize)]
+pub struct ResponseAppendWsRequest {
+    pub input: Vec<ResponseItem>,
+}
+#[derive(Debug, Serialize)]
+#[serde(tag = "type")]
+#[allow(clippy::large_enum_variant)]
+pub enum ResponsesWsRequest {
+    #[serde(rename = "response.create")]
+    ResponseCreate(ResponseCreateWsRequest),
+    #[serde(rename = "response.append")]
+    ResponseAppend(ResponseAppendWsRequest),
+}
+
 pub fn create_text_param_for_request(
     verbosity: Option<VerbosityConfig>,
     output_schema: &Option<Value>,