Add stdout Logging Support for headless Mode in TUI Installer

## Motivation

- When running TUI installer in non-interactive mode (`--non-interactive`), logs are not visible to users
- Non-interactive mode is typically used in CI/CD pipelines or automated deployments where stdout logging is essential
- Need to provide real-time feedback and debugging capability in headless environments

## Required Features

- **Non-Interactive Detection**: Track `non_interactive` flag in widget initialization
- **Unified Write Method**: Implement `_write_to_stdout()` method to handle various content types
- **Error Resilience**: Wrap stdout writes in try-except to prevent logging failures from interrupting installation

## Impact

- Improves debugging capability for non-interactive installations
- Provides consistent logging experience across interactive and non-interactive modes

JIRA Issue: BA-3803