I doubt Putin cares too much about the Olympics. In 2008 he occupied Georgia the day before the summer Olympics opened.
I can't keep from thinking that Putin may have a plan/agreement with China where he would take Ukraine, or part of it, and distract the U.S. to move men and equipment there, or near there, at which point China would attack Taiwan. It would be a win-win for Putin and China. But the Chinese want the propaganda win of the Olympics to finish first.