BOSTON—Russia accounted for most state-sponsored hacking detected by Microsoft over the past year, with a 58 percent share, mostly targeting government agencies and think tanks in the United States, followed by Ukraine, Britain, and European NATO members, the company said. The devastating effectiveness of the long-undetected SolarWinds hack—it mainly breached information technology businesses including Microsoft—also boosted Russian state-backed hackers’ success rate to 32 percent in the year ending June 30, compared with 21 percent in the preceding 12 months. China, meanwhile, accounted for fewer than 1 in 10 of the state-backed hacking attempts Microsoft detected but was successful 44 percent of the time in breaking into targeted networks, Microsoft said in its second annual Digital Defense Report, which covers July 2020 through June 2021. While Russia’s prolific state-sponsored hacking is well known, Microsoft’s report offers unusually specific detail on how it stacks up against that by other U.S. adversaries. The …