Avoid requesting key-release events in Ghostty (#36834)

## Why

Ghostty can leak release events for shortcuts that the terminal consumes.

## What changed

- Detect Ghostty when `TERM` is `xterm-ghostty`, including when `TERM_PROGRAM` is unavailable.
- Omit `REPORT_EVENT_TYPES` from keyboard enhancement flags for Ghostty while retaining alternate-key and escape-code disambiguation reporting.

## Testing

- Cover Ghostty detection through `TERM` and its keyboard enhancement flags.

GitOrigin-RevId: d865a6cdd1373aad4b78099e821d1ebaeb6cfdff

codex-rs/terminal-detection/src/lib.rs

@@ -150,6 +150,7 @@ impl TerminalInfo {
     fn from_term(term: String, multiplexer: Option<Multiplexer>) -> Self {
         let name = match term.as_str() {
             "dumb" => TerminalName::Dumb,
+            "xterm-ghostty" => TerminalName::Ghostty,
             "wezterm" | "wezterm-mux" => TerminalName::WezTerm,
             _ => TerminalName::Unknown,
         };
@@ -293,7 +294,7 @@ pub fn terminal_info() -> TerminalInfo {
 /// - Otherwise, `TERM_PROGRAM` (plus `TERM_PROGRAM_VERSION`) drives the detected terminal name.
 ///   This means `TERM_PROGRAM` can mask later probes (for example `WT_SESSION`).
 /// - Next, terminal-specific variables (WEZTERM, iTerm2, Apple Terminal, kitty, etc.) are checked.
-/// - Finally, `TERM` is used as the capability fallback with `TerminalName::Unknown`.
+/// - Finally, `TERM` is used as the capability fallback.
 ///
 /// tmux client term info is only consulted when a tmux multiplexer is detected, and it is
 /// derived from `tmux display-message` to surface the underlying terminal program instead of

codex-rs/terminal-detection/src/terminal_tests.rs

@@ -239,6 +239,25 @@ fn detects_ghostty() {
         "Ghostty",
         "ghostty_term_program_user_agent"
     );
+
+    let env = FakeEnvironment::new().with_var("TERM", "xterm-ghostty");
+    let terminal = detect_terminal_info_from_env(&env);
+    assert_eq!(
+        terminal,
+        terminal_info(
+            TerminalName::Ghostty,
+            /*term_program*/ None,
+            /*version*/ None,
+            Some("xterm-ghostty"),
+            /*multiplexer*/ None
+        ),
+        "ghostty_term_info"
+    );
+    assert_eq!(
+        terminal.user_agent_token(),
+        "xterm-ghostty",
+        "ghostty_term_user_agent"
+    );
 }
 
 #[test]