Render Markdown web links as labels in Rex (#53725)

## What changed

Select label-only web link rendering when `TERM_PROGRAM` is `rex`, matched case-insensitively. Preserve the existing visible-destination fallback for multiplexers and `dumb`, `screen`, or `tmux` terminal modes.

## Testing

Add a regression test verifying that Rex renders `[label](https://example.com)` with the label-only policy.

GitOrigin-RevId: 615ca6186d84fc17cef9286e75848877b542b6ab

codex-rs/tui/src/markdown_render/web_links.rs

@@ -69,6 +69,13 @@ impl WebLinkDisplay {
         {
             return Self::WithDestination;
         }
+        if terminal
+            .term_program
+            .as_deref()
+            .is_some_and(|program| program.eq_ignore_ascii_case("rex"))
+        {
+            return Self::LabelOnly;
+        }
         match terminal.name {
             TerminalName::Ghostty
             | TerminalName::Iterm2

codex-rs/tui/src/markdown_render/web_links_tests.rs

@@ -143,6 +143,21 @@ fn supporting_terminals_render_only_the_styled_label_and_keep_its_target() {
     }
 }
 
+#[test]
+fn rex_renders_only_the_label() {
+    let mut rex = terminal(TerminalName::Unknown);
+    rex.term_program = Some("rex".to_string());
+    let markdown = "[label](https://example.com)";
+    assert_eq!(
+        render(
+            markdown,
+            /*width*/ 80,
+            WebLinkDisplay::for_terminal(&rex, /*term*/ None),
+        ),
+        render(markdown, /*width*/ 80, WebLinkDisplay::LabelOnly),
+    );
+}
+
 #[test]
 fn unknown_terminals_and_multiplexers_keep_visible_destinations() {
     let mut tmux = terminal(TerminalName::Ghostty);