[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/tests/suite/compact_remote.rs

@@ -157,6 +157,7 @@ fn format_labeled_requests_snapshot(
 
 fn compacted_summary_only_output(summary: &str) -> Vec<ResponseItem> {
     vec![ResponseItem::Compaction {
+        id: None,
         encrypted_content: summary_with_prefix(summary),
         metadata: None,
     }]
@@ -329,6 +330,7 @@ async fn remote_compact_replaces_history_for_followups() -> Result<()> {
     .await;
 
     let compacted_history = vec![ResponseItem::Compaction {
+        id: None,
         encrypted_content: "ENCRYPTED_COMPACTION_SUMMARY".to_string(),
         metadata: None,
     }];
@@ -2356,6 +2358,7 @@ async fn remote_compact_persists_replacement_history_in_rollout() -> Result<()>
 
     let compacted_history = vec![
         ResponseItem::Compaction {
+            id: None,
             encrypted_content: "ENCRYPTED_COMPACTION_SUMMARY".to_string(),
             metadata: None,
         },
@@ -2511,6 +2514,7 @@ async fn remote_compact_and_resume_refresh_stale_developer_instructions() -> Res
             metadata: None,
         },
         ResponseItem::Compaction {
+            id: None,
             encrypted_content: "ENCRYPTED_COMPACTION_SUMMARY".to_string(),
             metadata: None,
         },
@@ -2653,6 +2657,7 @@ async fn remote_compact_refreshes_stale_developer_instructions_without_resume()
             metadata: None,
         },
         ResponseItem::Compaction {
+            id: None,
             encrypted_content: "ENCRYPTED_COMPACTION_SUMMARY".to_string(),
             metadata: None,
         },
@@ -4059,6 +4064,7 @@ async fn snapshot_request_shape_remote_mid_turn_compaction_summary_only_reinject
     .await;
 
     let compacted_history = vec![ResponseItem::Compaction {
+        id: None,
         encrypted_content: summary_with_prefix("REMOTE_SUMMARY_ONLY"),
         metadata: None,
     }];