[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/codex-api/src/requests/responses.rs

@@ -17,7 +17,7 @@ pub(crate) fn attach_item_ids(payload_json: &mut Value, original_items: &[Respon
     };
 
     for (value, item) in items.iter_mut().zip(original_items.iter()) {
-        if let ResponseItem::Reasoning { id, .. }
+        if let ResponseItem::Reasoning { id: Some(id), .. }
         | ResponseItem::Message { id: Some(id), .. }
         | ResponseItem::WebSearchCall { id: Some(id), .. }
         | ResponseItem::FunctionCall { id: Some(id), .. }