Connecticut shed 266,300 jobs in April, a record single-month loss that highlighted the devastating toll of the coronavirus crisis, according to preliminary numbers released Thursday by the state Department of Labor. Since March 13, the labor department has received more than 535,000 unemployment insurance applications — about the same amount that it would typically receive in a three-year period. About 38.6 million people have filed for jobless aid since the COVID-19 pandemic took hold, according to the U.S. Labor Department. Last month, U.S. employers cut about 20 million jobs, wiping out a decade’s worth of job growth in a single month. The unemployment rate soared to 14.7 percent, the highest level since the Depression.