WASHINGTON—The Biden administration on Thursday announced that people with Medicare will be able to get free over-the-counter tests much more easily in the coming weeks. The Centers for Medicare & Medicaid Services said Medicare will cover up to eight free tests per month, starting in early spring. The tests will be handed out at participating pharmacies and other locations. They will be available to people who have Medicare’s “Part B” outpatient benefit, which about 9 in 10 enrollees sign up for. Last month, the administration directed private insurers to cover up to eight free tests a month for people on their plans. Officials said at the time they were still trying to figure out what to do about Medicare, which covers more than 60 million people, most of them age 65 or older and more vulnerable to severe illness from coronavirus infection. Medicare benefits are governed by arcane laws and …