feat: add exit slash command alias for quit (#6002)

## Summary
- add the `/exit` slash command alongside `/quit` and reuse shared exit
handling
- refactor the chat widget to funnel quit, exit, logout, and shutdown
flows through a common `request_exit` helper
- add focused unit tests that confirm both `/quit` and `/exit` send an
`ExitRequest`

## Testing
- `just fmt`
- `just fix -p codex-tui`
- `cargo test -p codex-tui`


------
https://chatgpt.com/codex/tasks/task_i_6903d5a8f47c8321bf180f031f2fa330

codex-rs/tui/src/chatwidget.rs

@@ -657,7 +657,7 @@ impl ChatWidget {
     }
 
     fn on_shutdown_complete(&mut self) {
-        self.app_event_tx.send(AppEvent::ExitRequest);
+        self.request_exit();
     }
 
     fn on_turn_diff(&mut self, unified_diff: String) {
@@ -1229,8 +1229,8 @@ impl ChatWidget {
             SlashCommand::Approvals => {
                 self.open_approvals_popup();
             }
-            SlashCommand::Quit => {
-                self.app_event_tx.send(AppEvent::ExitRequest);
+            SlashCommand::Quit | SlashCommand::Exit => {
+                self.request_exit();
             }
             SlashCommand::Logout => {
                 if let Err(e) = codex_core::auth::logout(
@@ -1239,7 +1239,7 @@ impl ChatWidget {
                 ) {
                     tracing::error!("failed to logout: {e}");
                 }
-                self.app_event_tx.send(AppEvent::ExitRequest);
+                self.request_exit();
             }
             SlashCommand::Undo => {
                 self.app_event_tx.send(AppEvent::CodexOp(Op::Undo));
@@ -1593,6 +1593,10 @@ impl ChatWidget {
         }
     }
 
+    fn request_exit(&self) {
+        self.app_event_tx.send(AppEvent::ExitRequest);
+    }
+
     fn request_redraw(&mut self) {
         self.frame_requester.schedule_frame();
     }