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/memories/write/src/start.rs

@@ -0,0 +1,55 @@
+use crate::phase1;
+use crate::phase2;
+use crate::runtime::MemoryStartupContext;
+use codex_core::CodexThread;
+use codex_core::ThreadManager;
+use codex_core::config::Config;
+use codex_features::Feature;
+use codex_login::AuthManager;
+use codex_protocol::ThreadId;
+use codex_protocol::protocol::SessionSource;
+use std::sync::Arc;
+use tracing::warn;
+
+/// Starts the asynchronous startup memory pipeline for an eligible root session.
+///
+/// The pipeline is skipped for ephemeral sessions, disabled feature flags, and
+/// subagent sessions.
+pub fn start_memories_startup_task(
+    thread_manager: Arc<ThreadManager>,
+    auth_manager: Arc<AuthManager>,
+    thread_id: ThreadId,
+    thread: Arc<CodexThread>,
+    config: Arc<Config>,
+    source: &SessionSource,
+) {
+    if config.ephemeral
+        || !config.features.enabled(Feature::MemoryTool)
+        || source.is_non_root_agent()
+    {
+        return;
+    }
+
+    let context = Arc::new(MemoryStartupContext::new(
+        thread_manager,
+        auth_manager,
+        thread_id,
+        thread,
+        config.as_ref(),
+        source.clone(),
+    ));
+
+    if context.state_db().is_none() {
+        warn!("state db unavailable for memories startup pipeline; skipping");
+        return;
+    }
+
+    tokio::spawn(async move {
+        // Clean memories to make preserve DB size
+        phase1::prune(context.as_ref(), &config).await;
+        // Run phase 1.
+        phase1::run(Arc::clone(&context), Arc::clone(&config)).await;
+        // Run phase 2.
+        phase2::run(context, config).await;
+    });
+}