Russia has issued carefully calibrated criticism of both sides in the war between Israel and Hamas. But the conflict also is giving Moscow bold new opportunities — to advance its role as a global power broker and challenge Western efforts to isolate it over Ukraine. While Moscow lacks leverage to mediate a settlement in the Middle East, it could try to play on some perceived credibility problems with the West’s response to the crisis. It also expects the Israel-Hamas war to distract attention from the fighting in Ukraine and erode support for Kyiv. There are risks for Moscow, however. It...