WASHINGTON—U.S. services industry activity raced to its highest level in nearly two years in January, with growth in new orders and employment accelerating, raising cautious optimism that the beleaguered sector was turning the corner. The Institute for Supply Management (ISM) said on Feb. 3 its non-manufacturing activity index increased to a reading of 58.7 last month. That was the highest reading since February 2019 and followed 57.7 in December. The index is now above its pre-pandemic level. A reading above 50 indicates growth in the services sector, which accounts for more than two-thirds of U.S. economic activity. Economists polled by Reuters had forecast the index at 56.8. The ISM revised data going back to January 2012. The services industry has borne the brunt of the COVID-19 pandemic, which has forced authorities to impose restrictions on businesses like restaurants and bars. Consumers have also stayed away from other businesses and venues …