Add logout command to CLI and TUI (#1932)

## Summary
- support `codex logout` via new subcommand and helper that removes the
stored `auth.json`
- expose a `logout` function in `codex-login` and test it
- add `/logout` slash command in the TUI; command list is filtered when
not logged in and the handler deletes `auth.json` then exits

## Testing
- `just fix` *(fails: failed to get `diffy` from crates.io)*
- `cargo test --all-features` *(fails: failed to get `diffy` from
crates.io)*

------
https://chatgpt.com/codex/tasks/task_i_68945c3facac832ca83d48499716fb51

codex-rs/login/src/lib.rs

@@ -6,6 +6,7 @@ use serde::Serialize;
 use std::env;
 use std::fs::File;
 use std::fs::OpenOptions;
+use std::fs::remove_file;
 use std::io::Read;
 use std::io::Write;
 #[cfg(unix)]
@@ -185,6 +186,17 @@ fn get_auth_file(codex_home: &Path) -> PathBuf {
     codex_home.join("auth.json")
 }
 
+/// Delete the auth.json file inside `codex_home` if it exists. Returns `Ok(true)`
+/// if a file was removed, `Ok(false)` if no auth file was present.
+pub fn logout(codex_home: &Path) -> std::io::Result<bool> {
+    let auth_file = get_auth_file(codex_home);
+    match remove_file(&auth_file) {
+        Ok(_) => Ok(true),
+        Err(err) if err.kind() == std::io::ErrorKind::NotFound => Ok(false),
+        Err(err) => Err(err),
+    }
+}
+
 /// Represents a running login subprocess. The child can be killed by holding
 /// the mutex and calling `kill()`.
 #[derive(Debug, Clone)]
@@ -494,4 +506,15 @@ mod tests {
 
         assert!(auth.get_token_data().await.is_err());
     }
+
+    #[test]
+    fn logout_removes_auth_file() -> Result<(), std::io::Error> {
+        let dir = tempdir()?;
+        login_with_api_key(dir.path(), "sk-test-key")?;
+        assert!(dir.path().join("auth.json").exists());
+        let removed = logout(dir.path())?;
+        assert!(removed);
+        assert!(!dir.path().join("auth.json").exists());
+        Ok(())
+    }
 }