[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/compact_remote.rs

@@ -403,20 +403,24 @@ pub(crate) fn trim_function_call_history_to_fit_context_window(
 fn rewritten_output_for_context_window(item: &ResponseItem) -> Option<ResponseItem> {
     Some(match item {
         ResponseItem::FunctionCallOutput {
+            id,
             call_id,
             output,
             metadata,
         } => ResponseItem::FunctionCallOutput {
+            id: id.clone(),
             call_id: call_id.clone(),
             output: truncated_output_payload(output),
             metadata: metadata.clone(),
         },
         ResponseItem::CustomToolCallOutput {
+            id,
             call_id,
             name,
             output,
             metadata,
         } => ResponseItem::CustomToolCallOutput {
+            id: id.clone(),
             call_id: call_id.clone(),
             name: name.clone(),
             output: truncated_output_payload(output),
@@ -429,6 +433,7 @@ fn rewritten_output_for_context_window(item: &ResponseItem) -> Option<ResponseIt
             metadata,
             ..
         } => ResponseItem::ToolSearchOutput {
+            id: item.id().map(str::to_string),
             call_id: call_id.clone(),
             status: status.clone(),
             execution: execution.clone(),