simplify: use print! + flush for streamed chunks, not an explicit stdout lock

print! already locks stdout per call, so the manual lock()/write!() was
extra ceremony over what the flush actually needed. Matches rig's own
cli_chatbot streaming example more closely.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

deep_research/src/core.rs

@@ -178,7 +178,6 @@ async fn write_report(
     drop(spinner);
 
     let mut report = String::new();
-    let stdout = std::io::stdout();
 
     while let Some(chunk) = response_stream.next().await {
         match chunk? {
@@ -187,9 +186,11 @@ async fn write_report(
                 ..
             })) => {
                 report.push_str(&text);
-                let mut handle = stdout.lock();
+                // Terminal stdout is line-buffered, so a flush is needed here —
-                write!(handle, "{text}")?;
+                // otherwise a chunk without a trailing newline sits in the
-                handle.flush()?;
+                // buffer instead of appearing as it streams in.
+                print!("{text}");
+                std::io::stdout().flush()?;
             }
             _ => continue,
         }