feat: single app-server bootstrap in TUI (#16582)

Before this, the TUI was starting 2 app-server. One to check the login
status and one to actually start the session

This PR make only one app-server startup and defer the login check in
async, outside of the frame rendering path

---------

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

codex-rs/tui/src/onboarding/onboarding_screen.rs

@@ -447,7 +447,7 @@ impl WidgetRef for Step {
 
 pub(crate) async fn run_onboarding_app(
     args: OnboardingScreenArgs,
-    mut app_server: Option<AppServerSession>,
+    mut app_server: Option<&mut AppServerSession>,
     tui: &mut Tui,
 ) -> Result<OnboardingResult> {
     use tokio_stream::StreamExt;
@@ -533,9 +533,6 @@ pub(crate) async fn run_onboarding_app(
             }
         }
     }
-    if let Some(app_server) = app_server {
-        app_server.shutdown().await.ok();
-    }
     Ok(OnboardingResult {
         directory_trust_decision: onboarding_screen.directory_trust_decision(),
         should_exit: onboarding_screen.should_exit(),