fix: update brew auto update version check (#6238)

### Summary
* Use
`https://github.com/Homebrew/homebrew-cask/blob/main/Casks/c/codex.rb`
to get the latest available version for brew usage.

codex-rs/tui/src/update_action.rs

@@ -0,0 +1,101 @@
+/// Update action the CLI should perform after the TUI exits.
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub enum UpdateAction {
+    /// Update via `npm install -g @openai/codex@latest`.
+    NpmGlobalLatest,
+    /// Update via `bun install -g @openai/codex@latest`.
+    BunGlobalLatest,
+    /// Update via `brew upgrade codex`.
+    BrewUpgrade,
+}
+
+impl UpdateAction {
+    /// Returns the list of command-line arguments for invoking the update.
+    pub fn command_args(self) -> (&'static str, &'static [&'static str]) {
+        match self {
+            UpdateAction::NpmGlobalLatest => ("npm", &["install", "-g", "@openai/codex"]),
+            UpdateAction::BunGlobalLatest => ("bun", &["install", "-g", "@openai/codex"]),
+            UpdateAction::BrewUpgrade => ("brew", &["upgrade", "codex"]),
+        }
+    }
+
+    /// Returns string representation of the command-line arguments for invoking the update.
+    pub fn command_str(self) -> String {
+        let (command, args) = self.command_args();
+        shlex::try_join(std::iter::once(command).chain(args.iter().copied()))
+            .unwrap_or_else(|_| format!("{command} {}", args.join(" ")))
+    }
+}
+
+#[cfg(not(debug_assertions))]
+pub(crate) fn get_update_action() -> Option<UpdateAction> {
+    let exe = std::env::current_exe().unwrap_or_default();
+    let managed_by_npm = std::env::var_os("CODEX_MANAGED_BY_NPM").is_some();
+    let managed_by_bun = std::env::var_os("CODEX_MANAGED_BY_BUN").is_some();
+
+    detect_update_action(
+        cfg!(target_os = "macos"),
+        &exe,
+        managed_by_npm,
+        managed_by_bun,
+    )
+}
+
+#[cfg(any(not(debug_assertions), test))]
+fn detect_update_action(
+    is_macos: bool,
+    current_exe: &std::path::Path,
+    managed_by_npm: bool,
+    managed_by_bun: bool,
+) -> Option<UpdateAction> {
+    if managed_by_npm {
+        Some(UpdateAction::NpmGlobalLatest)
+    } else if managed_by_bun {
+        Some(UpdateAction::BunGlobalLatest)
+    } else if is_macos
+        && (current_exe.starts_with("/opt/homebrew") || current_exe.starts_with("/usr/local"))
+    {
+        Some(UpdateAction::BrewUpgrade)
+    } else {
+        None
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn detects_update_action_without_env_mutation() {
+        assert_eq!(
+            detect_update_action(false, std::path::Path::new("/any/path"), false, false),
+            None
+        );
+        assert_eq!(
+            detect_update_action(false, std::path::Path::new("/any/path"), true, false),
+            Some(UpdateAction::NpmGlobalLatest)
+        );
+        assert_eq!(
+            detect_update_action(false, std::path::Path::new("/any/path"), false, true),
+            Some(UpdateAction::BunGlobalLatest)
+        );
+        assert_eq!(
+            detect_update_action(
+                true,
+                std::path::Path::new("/opt/homebrew/bin/codex"),
+                false,
+                false
+            ),
+            Some(UpdateAction::BrewUpgrade)
+        );
+        assert_eq!(
+            detect_update_action(
+                true,
+                std::path::Path::new("/usr/local/bin/codex"),
+                false,
+                false
+            ),
+            Some(UpdateAction::BrewUpgrade)
+        );
+    }
+}