async def METHOD_NAME(context: ConnectorContext) -> ConnectorReport:
    """Run a format pipeline for a single connector.
    Args:
        context (ConnectorContext): The initialized connector context.
    Returns:
        ConnectorReport: The reports holding formats results.
    """
    steps_results = []
    async with context:
        FormatConnectorCode = FORMATTING_STEP_TO_CONNECTOR_LANGUAGE_MAPPING.get(context.connector.language)
        if not FormatConnectorCode:
            raise NoFormatStepForLanguageError(
                f"No formatting step found for connector {context.connector.technical_name} with language {context.connector.language}"
            )
        format_connector_code_result = await FormatConnectorCode(context).run()
        steps_results.append(format_connector_code_result)
        if context.is_local:
            export_changes_results = await ExportChanges(context).run(
                format_connector_code_result.output_artifact, str(context.connector.code_directory)
            )
            steps_results.append(export_changes_results)
        else:
            git_push_changes_results = await GitPushChanges(context).run(
                format_connector_code_result.output_artifact,
                str(context.connector.code_directory),
                f"Auto format {context.connector.technical_name} code",
                skip_ci=True,
            )
            steps_results.append(git_push_changes_results)
        context.report = ConnectorReport(context, steps_results, name="FORMAT RESULTS")
    return context.report