What should we use to log important data?

You should use the Nest JS logger to log any important data in your app. You could generate a new instance of the logger for each server to add a context to the log.

async function bootstrap() {
  const app = await NestFactory.create(AppModule);

  const configService = app.get(ConfigService);
  const port = configService.get('PORT');

  await app.listen(port);
  const logger = new Logger('Synergy API');
  logger.log('Server start listening on port: ' + port);
}