Try using an Unbuffered sys.stderr

cibuildwheel/__main__.py

@@ -220,6 +220,7 @@ def main() -> None:
 
     # Python is buffering by default when running on the CI platforms, giving problems interleaving subprocess call output with unflushed calls to 'print'
     sys.stdout = Unbuffered(sys.stdout)  # type: ignore
+    sys.stderr = Unbuffered(sys.stderr)  # type: ignore
 
     print_preamble(platform, build_options)