[codex] Add optional IDs to response items (#28812)

## Why

`ResponseItem` variants do not have a consistent internal ID shape: some
variants carry required IDs, some carry optional IDs, and some cannot
represent an ID at all. The existing fields also use inconsistent serde,
TypeScript, and JSON-schema annotations. A single enum-level access path
is needed before history recording can assign and retain IDs.

This PR establishes that internal model only. It intentionally does not
generate or serialize IDs; allocation and wire persistence are isolated
in the stacked follow-up.

## What changed

- Give every concrete `ResponseItem` variant an `Option<String>` ID
field.
- Apply the same internal-only annotations to every ID field:
`#[serde(default, skip_serializing)]`, `#[ts(skip)]`, and
`#[schemars(skip)]`.
- Add `ResponseItem::id()` and `ResponseItem::set_id()` as the shared
accessors.
- Preserve IDs when history items are rewritten for truncation.
- Adapt consumers that previously assumed reasoning and image-generation
IDs were required.
- Regenerate app-server schemas so the hidden fields are represented
consistently.

The serde catch-all `ResponseItem::Other` remains ID-less because it
must remain a unit variant.

## Test plan

- `cargo check --tests -p codex-core -p codex-api -p codex-rollout-trace
-p codex-image-generation-extension`
- `just test -p codex-protocol`
- `just test -p codex-app-server-protocol`
- `just test -p codex-api -p codex-rollout-trace -p
codex-image-generation-extension`
- `just test -p codex-core event_mapping`

codex-rs/core/src/session/tests.rs

@@ -1664,6 +1664,7 @@ async fn resize_all_images_prepares_failures_before_history_insertion() {
     )
     .await;
     let item = ResponseItem::FunctionCallOutput {
+        id: None,
         call_id: "call-1".to_string(),
         output: FunctionCallOutputPayload {
             body: FunctionCallOutputBody::ContentItems(vec![
@@ -1689,6 +1690,7 @@ async fn resize_all_images_prepares_failures_before_history_insertion() {
         .await;
 
     let expected = vec![ResponseItem::FunctionCallOutput {
+        id: None,
         call_id: "call-1".to_string(),
         output: FunctionCallOutputPayload {
             body: FunctionCallOutputBody::ContentItems(vec![
@@ -7720,7 +7722,7 @@ async fn build_initial_context_omits_default_image_save_location_with_image_hist
     session
         .replace_history(
             vec![ResponseItem::ImageGenerationCall {
-                id: "ig-test".to_string(),
+                id: Some("ig-test".to_string()),
                 status: "completed".to_string(),
                 revised_prompt: Some("a tiny blue square".to_string()),
                 result: "Zm9v".to_string(),
@@ -7973,7 +7975,7 @@ async fn handle_output_item_done_records_image_save_history_message() {
     );
     let _ = std::fs::remove_file(&expected_saved_path);
     let item = ResponseItem::ImageGenerationCall {
-        id: call_id.to_string(),
+        id: Some(call_id.to_string()),
         status: "completed".to_string(),
         revised_prompt: Some("a tiny blue square".to_string()),
         result: "Zm9v".to_string(),
@@ -8030,7 +8032,7 @@ async fn handle_output_item_done_skips_image_save_message_when_save_fails() {
     );
     let _ = std::fs::remove_file(&expected_saved_path);
     let item = ResponseItem::ImageGenerationCall {
-        id: call_id.to_string(),
+        id: Some(call_id.to_string()),
         status: "completed".to_string(),
         revised_prompt: Some("broken payload".to_string()),
         result: "_-8".to_string(),