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/session/session.rs

@@ -425,10 +425,7 @@ impl Session {
             session_init.ephemeral = config.ephemeral,
         ));
 
-        let is_subagent = matches!(
-            session_configuration.session_source,
-            SessionSource::SubAgent(_)
-        );
+        let is_subagent = session_configuration.session_source.is_non_root_agent();
         let history_meta_fut = async {
             if is_subagent {
                 (0, 0)
@@ -989,12 +986,6 @@ impl Session {
                 state.set_pending_session_start_source(Some(session_start_source));
             }
 
-            memories::start_memories_startup_task(
-                &sess,
-                Arc::clone(&config),
-                &session_configuration.session_source,
-            );
-
             Ok(sess)
         }
         .await;