Send base instructions as Responses input messages (#51156)

## What changed

Move base instructions from the top-level `instructions` field into a prefixed `developer` message in `input` for standard Responses requests, matching Responses Lite. Remove the field from HTTP and WebSocket request types and assign instruction messages stable IDs derived from the thread and instruction text.

## Testing

Extend standard and Responses Lite tests to cover instruction message serialization, stable IDs, and resume consistency. Update WebSocket tests to verify that changed instructions trigger a full request without `previous_response_id`.

GitOrigin-RevId: e2de4b8e30a9339377fac133ceda981abd1a112b

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

@@ -283,8 +283,6 @@ pub struct ResponsesApiRequest {
     pub stream: bool,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub service_tier: Option<String>,
-    #[serde(skip_serializing_if = "String::is_empty")]
-    pub instructions: String,
     pub input: Vec<ResponseItem>,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub tools: Option<ResponsesApiTools>,
@@ -309,7 +307,6 @@ impl<'a> From<&'a ResponsesApiRequest> for ResponseCreateWsRequest<'a> {
     fn from(request: &'a ResponsesApiRequest) -> Self {
         Self {
             model: &request.model,
-            instructions: &request.instructions,
             previous_response_id: None,
             input: &request.input,
             tools: request.tools.as_ref().map(ResponsesApiTools::as_raw_value),
@@ -338,8 +335,6 @@ pub struct ResponseCreateWsRequest<'a> {
     pub stream: bool,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub service_tier: Option<&'a str>,
-    #[serde(skip_serializing_if = "str::is_empty")]
-    pub instructions: &'a str,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub previous_response_id: Option<String>,
     pub input: &'a [ResponseItem],

codex-rs/codex-api/src/endpoint/responses_websocket.rs

@@ -945,7 +945,6 @@ mod tests {
     fn direct_serialization_preserves_websocket_request_payload() {
         let api_request = ResponsesApiRequest {
             model: "gpt-test".to_string(),
-            instructions: "Use the available tools.".to_string(),
             input: vec![ResponseItem::Message {
                 id: Some(ResponseItemId::with_suffix("msg", "1")),
                 role: "user".to_string(),
@@ -998,7 +997,7 @@ mod tests {
         let request_text =
             serialize_websocket_request(&request).expect("serialize websocket request");
         assert!(request_text.starts_with(
-            r#"{"type":"response.create","model":"gpt-test","stream":true,"service_tier":"priority","instructions":"Use the available tools.","previous_response_id":"resp-1","input":"#
+            r#"{"type":"response.create","model":"gpt-test","stream":true,"service_tier":"priority","previous_response_id":"resp-1","input":"#
         ));
         let wire_payload =
             serde_json::from_str::<Value>(&request_text).expect("parse websocket request");