fix(logging): avoid race condition in live logging with background threads

[goingforstudying-ctrl]

Fixes #13693

Replace capture suspension in _LiveLoggingStreamHandler.emit() with direct writes to the original stdout stream. This prevents race conditions where background threads write to stdout/stderr while capture is suspended, causing lost output in capfd/capsys fixtures.

The previous implementation used capture_manager.global_and_fixture_disabled() which temporarily restored sys.stdout/stderr to their original values. When background threads logged during this window, their writes bypassed capture. The fix creates a temporary TerminalWriter pointing to the original stdout, allowing log messages to appear on the terminal while keeping capture active for all threads.

[goingforstudying-ctrl]

Pushed a fix for the test_live_logging_suspends_capture failure. The MockCaptureManager mock in the test needed a get_original_stdout() method to match the new API used by _LiveLoggingStreamHandler.emit(). Also removed the now-obsolete assertions on global_and_fixture_disabled call tracking since the handler no longer suspends capture.

Let me know if anything else needs adjustment.

[goingforstudying-ctrl]

Fixed the mypy error in get_original_stdout().

• Changed return type to TextIO | None since sys.__stdout__ can be None
• Added a None guard in _LiveLoggingStreamHandler.emit() before writing to the stream

Should be green now.