LONDON—Euro zone manufacturing growth slowed sharply last month as Russia’s invasion of Ukraine tightened supply chain bottlenecks, dampened demand, and whacked confidence, a survey showed as soaring energy costs drove a broader surge in prices. Uncertainty caused by the invasion combined with an intensifying cost-of-living crisis suggests the bloc’s manufacturing industry could slide into a recession this quarter. S&P Global’s final manufacturing Purchasing Managers’ Index (PMI) fell to a 14-month low of 56.5 in March from February’s 58.2, below an initial “flash” estimate of 57.0 but still well above the 50 mark that separates growth from contraction. An index measuring output, which feeds into a composite PMI due next week and is seen as a good barometer of economic health, sank to 53.1 from 55.5, its lowest since June 2020, when the bloc was enduring the first wave of the coronavirus pandemic. “Just as the fading of the latest pandemic …