[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/client_common_tests.rs

@@ -23,6 +23,7 @@ fn prompt_with_image_outputs() -> Prompt {
                 metadata: None,
             },
             ResponseItem::FunctionCallOutput {
+                id: None,
                 call_id: "function-call".to_string(),
                 output: FunctionCallOutputPayload::from_content_items(vec![
                     FunctionCallOutputContentItem::InputImage {
@@ -33,6 +34,7 @@ fn prompt_with_image_outputs() -> Prompt {
                 metadata: None,
             },
             ResponseItem::CustomToolCallOutput {
+                id: None,
                 call_id: "custom-call".to_string(),
                 name: None,
                 output: FunctionCallOutputPayload::from_content_items(vec![
@@ -69,6 +71,7 @@ fn responses_lite_request_copies_strip_image_details() {
                 metadata: None,
             },
             ResponseItem::FunctionCallOutput {
+                id: None,
                 call_id: "function-call".to_string(),
                 output: FunctionCallOutputPayload::from_content_items(vec![
                     FunctionCallOutputContentItem::InputImage {
@@ -79,6 +82,7 @@ fn responses_lite_request_copies_strip_image_details() {
                 metadata: None,
             },
             ResponseItem::CustomToolCallOutput {
+                id: None,
                 call_id: "custom-call".to_string(),
                 name: None,
                 output: FunctionCallOutputPayload::from_content_items(vec![