[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_v2.rs

@@ -231,7 +231,10 @@ async fn run_remote_compact_task_inner_impl(
     )
     .await?;
     let mut input = prompt_input.clone();
-    input.push(ResponseItem::CompactionTrigger { metadata: None });
+    input.push(ResponseItem::CompactionTrigger {
+        id: None,
+        metadata: None,
+    });
     let prompt = Prompt {
         input,
         tools: tool_router.model_visible_specs(),
@@ -609,11 +612,13 @@ mod tests {
                 metadata: None,
             },
             ResponseItem::Compaction {
+                id: None,
                 encrypted_content: "old".to_string(),
                 metadata: None,
             },
         ];
         let output = ResponseItem::Compaction {
+            id: None,
             encrypted_content: "new".to_string(),
             metadata: None,
         };
@@ -642,6 +647,7 @@ mod tests {
             new.clone(),
         ];
         let output = ResponseItem::Compaction {
+            id: None,
             encrypted_content: "new".to_string(),
             metadata: None,
         };
@@ -673,6 +679,7 @@ mod tests {
             metadata: None,
         }];
         let output = ResponseItem::Compaction {
+            id: None,
             encrypted_content: "new".to_string(),
             metadata: None,
         };
@@ -800,6 +807,7 @@ mod tests {
     #[tokio::test]
     async fn collect_compaction_output_accepts_additional_output_items() {
         let compaction = ResponseItem::Compaction {
+            id: None,
             encrypted_content: "encrypted".to_string(),
             metadata: None,
         };