From February 2020 through January, Medicaid enrollment climbed nationwide by 9.7 million, according to a report, based on the most recent available data, released Monday by the Centers for Medicare and Medicaid Services. Some people signed up last year as the pandemic’s economic fallout took away their jobs, income and health benefits. But according to federal health officials and other Medicaid experts, much of the increase is because of a rule change that was part of the first coronavirus relief law adopted by Congress last year. That law created a trade-off: It gave states extra federal money to help cover what were anticipated to be ballooning Medicaid costs. In exchange, states needed to promise they would not remove anyone from their Medicaid rolls until the federal government ended the coronavirus public health emergency. Taken together, the 15 percent spike means the size of the public insurance program for low-income Americans now significantly eclipses the nearly 63 million older Americans covered last year through Medicare.