Add ad-hoc memory note tool (#24562)

## Why

Codex memory updates currently rely on instructions that tell agents to
create ad-hoc note files directly in the memory workspace. The memories
extension already has a `MemoriesBackend` abstraction for local storage
and future non-filesystem backends, so the ad-hoc note writer should
live behind that same interface instead of baking local filesystem
assumptions into the tool shape.

## What

- Adds a `memories/add_ad_hoc_note` tool to the existing memories tool
bundle.
- Extends `MemoriesBackend` with `add_ad_hoc_note` plus request/response
types so remote memory stores can implement the same operation later.
- Implements the local backend by creating append-only notes under
`extensions/ad_hoc/notes`.
- Validates the tool-provided filename contract
(`YYYY-MM-DDTHH-MM-SS-<slug>.md`), rejects path-like filenames, rejects
empty notes, and uses create-new semantics so existing notes are never
overwritten.
- Keeps memories tool contribution behind the existing commented-out
registration path; this defines the tool surface without newly exposing
it through app-server.

## Test Plan

- `just test -p codex-memories-extension`

codex-rs/ext/memories/src/tests.rs

@@ -69,6 +69,7 @@ fn tools_are_contributed_when_enabled() {
     assert_eq!(
         tool_names,
         vec![
+            memory_tool_name(crate::ADD_AD_HOC_NOTE_TOOL_NAME),
             memory_tool_name(crate::LIST_TOOL_NAME),
             memory_tool_name(crate::READ_TOOL_NAME),
             memory_tool_name(crate::SEARCH_TOOL_NAME),
@@ -76,6 +77,26 @@ fn tools_are_contributed_when_enabled() {
     );
 }
 
+#[test]
+fn ad_hoc_tool_definition_includes_filename_contract() {
+    let tool = memory_tool(
+        Path::new("/tmp/codex-home/memories"),
+        crate::ADD_AD_HOC_NOTE_TOOL_NAME,
+    );
+    let spec = serde_json::to_value(tool.spec()).expect("serialize tool spec");
+
+    let filename = spec
+        .pointer("/tools/0/parameters/properties/filename")
+        .expect("filename parameter should be in tool schema");
+    assert_eq!(filename.pointer("/type"), Some(&json!("string")));
+    assert!(
+        filename
+            .pointer("/description")
+            .and_then(serde_json::Value::as_str)
+            .is_some_and(|description| description.contains("YYYY-MM-DDTHH-MM-SS-<slug>.md"))
+    );
+}
+
 #[tokio::test]
 async fn prompt_contribution_uses_memory_summary_when_enabled() {
     let tempdir = tempfile::tempdir().expect("tempdir");
@@ -110,6 +131,79 @@ async fn prompt_contribution_uses_memory_summary_when_enabled() {
     );
 }
 
+#[tokio::test]
+async fn add_ad_hoc_note_tool_creates_note_file() {
+    let tempdir = tempfile::tempdir().expect("tempdir");
+    let memory_root = tempdir.path().join("memories");
+    let tool = memory_tool(&memory_root, crate::ADD_AD_HOC_NOTE_TOOL_NAME);
+    let payload = ToolPayload::Function {
+        arguments: json!({
+            "filename": "2026-05-26T13-42-08-remember-review-style.md",
+            "note": "Remember to keep PR review comments concise.",
+        })
+        .to_string(),
+    };
+
+    let output = tool
+        .handle(ToolCall {
+            turn_id: "turn-1".to_string(),
+            call_id: "call-1".to_string(),
+            tool_name: memory_tool_name(crate::ADD_AD_HOC_NOTE_TOOL_NAME),
+            truncation_policy: TruncationPolicy::Bytes(1024),
+            conversation_history: codex_extension_api::ConversationHistory::default(),
+            payload: payload.clone(),
+        })
+        .await
+        .expect("ad-hoc note should be written");
+
+    assert_eq!(
+        output.post_tool_use_response("call-1", &payload),
+        Some(json!({}))
+    );
+    assert_eq!(
+        tokio::fs::read_to_string(
+            memory_root
+                .join("extensions/ad_hoc/notes")
+                .join("2026-05-26T13-42-08-remember-review-style.md")
+        )
+        .await
+        .expect("read ad-hoc note"),
+        "Remember to keep PR review comments concise."
+    );
+}
+
+#[tokio::test]
+async fn add_ad_hoc_note_tool_rejects_paths_as_filenames() {
+    let tempdir = tempfile::tempdir().expect("tempdir");
+    let memory_root = tempdir.path().join("memories");
+    let tool = memory_tool(&memory_root, crate::ADD_AD_HOC_NOTE_TOOL_NAME);
+    let payload = ToolPayload::Function {
+        arguments: json!({
+            "filename": "../2026-05-26T13-42-08-remember-review-style.md",
+            "note": "Remember to keep PR review comments concise.",
+        })
+        .to_string(),
+    };
+
+    let result = tool
+        .handle(ToolCall {
+            turn_id: "turn-1".to_string(),
+            call_id: "call-1".to_string(),
+            tool_name: memory_tool_name(crate::ADD_AD_HOC_NOTE_TOOL_NAME),
+            truncation_policy: TruncationPolicy::Bytes(1024),
+            conversation_history: codex_extension_api::ConversationHistory::default(),
+            payload,
+        })
+        .await;
+    let err = match result {
+        Ok(_) => panic!("path-like filename should be rejected"),
+        Err(err) => err,
+    };
+
+    assert!(err.to_string().contains("filename"));
+    assert!(err.to_string().contains("YYYY-MM-DDTHH-MM-SS"));
+}
+
 #[tokio::test]
 async fn read_tool_reads_memory_file() {
     let tempdir = tempfile::tempdir().expect("tempdir");