Russian government hackers breached the computer systems of the Republican National Committee last week, around the time a Russia-linked criminal group unleashed a massive ransomware attack, according to two people familiar with the matter. The government hackers were part of a group known as APT 29 or Cozy Bear, according to the people. That group has been tied to Russia’s foreign intelligence service and has previously been accused of breaching the Democratic National Committee in 2016 and of carrying out a supply-chain cyberattack involving SolarWinds Corp., which infiltrated nine U.S. government agencies and was disclosed in December. It’s not known...