Persist and prewarm agent tasks per thread (#17978)

## Summary
- persist registered agent tasks in the session state update stream so
the thread can reuse them
- prewarm task registration once identity registration succeeds, while
keeping startup failures best-effort
- isolate the session-side task lifecycle into a dedicated module so
AgentIdentityManager and RegisteredAgentTask do not leak across as many
core layers

## Testing
- cargo test -p codex-core startup_agent_task_prewarm
- cargo test -p codex-core
cached_agent_task_for_current_identity_clears_stale_task
- cargo test -p codex-core record_initial_history_

codex-rs/core/src/state/session_tests.rs

@@ -1,8 +1,8 @@
 use super::*;
-use crate::agent_identity::RegisteredAgentTask;
 use crate::session::tests::make_session_configuration_for_tests;
 use codex_protocol::protocol::CreditsSnapshot;
 use codex_protocol::protocol::RateLimitWindow;
+use codex_protocol::protocol::SessionAgentTask;
 use pretty_assertions::assert_eq;
 
 #[tokio::test]
@@ -38,11 +38,8 @@ async fn clear_connector_selection_removes_entries() {
 async fn set_agent_task_persists_plaintext_task_for_session_reuse() {
     let session_configuration = make_session_configuration_for_tests().await;
     let mut state = SessionState::new(session_configuration);
-    let agent_task = RegisteredAgentTask {
-        binding_id: "chatgpt-account-account-123".to_string(),
-        chatgpt_account_id: "account-123".to_string(),
-        chatgpt_user_id: Some("user-123".to_string()),
-        agent_runtime_id: "agent_123".to_string(),
+    let agent_task = SessionAgentTask {
+        agent_runtime_id: "agent-123".to_string(),
         task_id: "task_123".to_string(),
         registered_at: "2026-03-23T12:00:00Z".to_string(),
     };
@@ -56,10 +53,7 @@ async fn set_agent_task_persists_plaintext_task_for_session_reuse() {
 async fn clear_agent_task_removes_cached_task() {
     let session_configuration = make_session_configuration_for_tests().await;
     let mut state = SessionState::new(session_configuration);
-    let agent_task = RegisteredAgentTask {
-        binding_id: "chatgpt-account-account-123".to_string(),
-        chatgpt_account_id: "account-123".to_string(),
-        chatgpt_user_id: Some("user-123".to_string()),
+    let agent_task = SessionAgentTask {
         agent_runtime_id: "agent_123".to_string(),
         task_id: "task_123".to_string(),
         registered_at: "2026-03-23T12:00:00Z".to_string(),