Show ChatGPT login URL during onboarding (#2028)

## Summary
- display authentication URL in the ChatGPT sign-in screen while
onboarding

<img width="684" height="151" alt="image"
src="https://github.com/user-attachments/assets/a8c32cb0-77f6-4a3f-ae3b-6695247c994d"
/>

codex-rs/login/src/lib.rs

@@ -9,6 +9,7 @@ use std::fs::OpenOptions;
 use std::fs::remove_file;
 use std::io::Read;
 use std::io::Write;
+use std::io::{self};
 #[cfg(unix)]
 use std::os::unix::fs::OpenOptionsExt;
 use std::path::Path;
@@ -262,6 +263,50 @@ pub struct SpawnedLogin {
     pub stderr: Arc<Mutex<Vec<u8>>>,
 }
 
+impl SpawnedLogin {
+    /// Returns the login URL, if one has been emitted by the login subprocess.
+    ///
+    /// The Python helper prints the URL to stderr; we capture it and extract
+    /// the last whitespace-separated token that starts with "http".
+    pub fn get_login_url(&self) -> Option<String> {
+        self.stderr
+            .lock()
+            .ok()
+            .and_then(|buffer| String::from_utf8(buffer.clone()).ok())
+            .and_then(|output| {
+                output
+                    .split_whitespace()
+                    .filter(|part| part.starts_with("http"))
+                    .next_back()
+                    .map(|s| s.to_string())
+            })
+    }
+}
+
+// Helpers for streaming child output into shared buffers
+struct AppendWriter {
+    buf: Arc<Mutex<Vec<u8>>>,
+}
+
+impl Write for AppendWriter {
+    fn write(&mut self, data: &[u8]) -> io::Result<usize> {
+        if let Ok(mut b) = self.buf.lock() {
+            b.extend_from_slice(data);
+        }
+        Ok(data.len())
+    }
+
+    fn flush(&mut self) -> io::Result<()> {
+        Ok(())
+    }
+}
+
+fn spawn_pipe_reader<R: Read + Send + 'static>(mut reader: R, buf: Arc<Mutex<Vec<u8>>>) {
+    std::thread::spawn(move || {
+        let _ = io::copy(&mut reader, &mut AppendWriter { buf });
+    });
+}
+
 /// Spawn the ChatGPT login Python server as a child process and return a handle to its process.
 pub fn spawn_login_with_chatgpt(codex_home: &Path) -> std::io::Result<SpawnedLogin> {
     let script_path = write_login_script_to_disk()?;
@@ -278,25 +323,11 @@ pub fn spawn_login_with_chatgpt(codex_home: &Path) -> std::io::Result<SpawnedLog
     let stdout_buf = Arc::new(Mutex::new(Vec::new()));
     let stderr_buf = Arc::new(Mutex::new(Vec::new()));
 
-    if let Some(mut out) = child.stdout.take() {
-        let buf = stdout_buf.clone();
-        std::thread::spawn(move || {
-            let mut tmp = Vec::new();
-            let _ = std::io::copy(&mut out, &mut tmp);
-            if let Ok(mut b) = buf.lock() {
-                b.extend_from_slice(&tmp);
-            }
-        });
+    if let Some(out) = child.stdout.take() {
+        spawn_pipe_reader(out, stdout_buf.clone());
     }
-    if let Some(mut err) = child.stderr.take() {
-        let buf = stderr_buf.clone();
-        std::thread::spawn(move || {
-            let mut tmp = Vec::new();
-            let _ = std::io::copy(&mut err, &mut tmp);
-            if let Ok(mut b) = buf.lock() {
-                b.extend_from_slice(&tmp);
-            }
-        });
+    if let Some(err) = child.stderr.take() {
+        spawn_pipe_reader(err, stderr_buf.clone());
     }
 
     Ok(SpawnedLogin {