feat: split memories part 2 (#19860)

Keep extracting memories out of core and moving the write trigger in the
app-server
This is temporary and it should move at the client level as a follow-up
This makes core fully independant from `codex-memories-write`

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/core/src/client_tests.rs

@@ -18,6 +18,7 @@ use codex_protocol::ThreadId;
 use codex_protocol::models::ContentItem;
 use codex_protocol::models::ResponseItem;
 use codex_protocol::openai_models::ModelInfo;
+use codex_protocol::protocol::InternalSessionSource;
 use codex_protocol::protocol::SessionSource;
 use codex_protocol::protocol::SubAgentSource;
 use codex_rollout_trace::ExecutionStatus;
@@ -197,6 +198,18 @@ fn build_subagent_headers_sets_other_subagent_label() {
     assert_eq!(value, Some("memory_consolidation"));
 }
 
+#[test]
+fn build_subagent_headers_sets_internal_memory_consolidation_label() {
+    let client = test_model_client(SessionSource::Internal(
+        InternalSessionSource::MemoryConsolidation,
+    ));
+    let headers = client.build_subagent_headers();
+    let value = headers
+        .get(X_OPENAI_SUBAGENT_HEADER)
+        .and_then(|value| value.to_str().ok());
+    assert_eq!(value, Some("memory_consolidation"));
+}
+
 #[test]
 fn build_ws_client_metadata_includes_window_lineage_and_turn_metadata() {
     let parent_thread_id = ThreadId::new();