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/slash_command.rs

@@ -25,6 +25,7 @@ pub enum SlashCommand {
     Mcp,
     Logout,
     Quit,
+    Exit,
     Feedback,
     Rollout,
     TestApproval,
@@ -40,7 +41,7 @@ impl SlashCommand {
             SlashCommand::Compact => "summarize conversation to prevent hitting the context limit",
             SlashCommand::Review => "review my current changes and find issues",
             SlashCommand::Undo => "ask Codex to undo a turn",
-            SlashCommand::Quit => "exit Codex",
+            SlashCommand::Quit | SlashCommand::Exit => "exit Codex",
             SlashCommand::Diff => "show git diff (including untracked files)",
             SlashCommand::Mention => "mention a file",
             SlashCommand::Status => "show current session configuration and token usage",
@@ -75,7 +76,8 @@ impl SlashCommand {
             | SlashCommand::Status
             | SlashCommand::Mcp
             | SlashCommand::Feedback
-            | SlashCommand::Quit => true,
+            | SlashCommand::Quit
+            | SlashCommand::Exit => true,
             SlashCommand::Rollout => true,
             SlashCommand::TestApproval => true,
         }