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/app-server/tests/suite/v2/initialize.rs

@@ -24,7 +24,9 @@ use std::time::Duration;
 use tempfile::TempDir;
 use tokio::time::timeout;
 
-const DEFAULT_READ_TIMEOUT: std::time::Duration = std::time::Duration::from_secs(10);
+// This covers debug app-server process startup before the first JSON-RPC response,
+// not expected steady-state request latency.
+const DEFAULT_READ_TIMEOUT: std::time::Duration = std::time::Duration::from_secs(20);
 
 #[tokio::test]
 async fn initialize_uses_client_info_name_as_originator() -> Result<()> {