LONDON—The eurozone economic recovery weakened this month, despite an upturn in Germany where factories benefited from an easing in supply chain bottlenecks, as renewed restrictions put a dent in the bloc’s dominant services industry, a survey showed. With the Omicron coronavirus variant sweeping across Europe, governments have been encouraging citizens to stay home and avoid socializing while soaring prices have discouraged consumers from spending. HIS Markit’s Flash Composite Purchasing Managers’ Index, seen as a good gauge of overall economic health, dropped to 52.4 in January from 53.3 in December, its lowest since February and below the 52.6 predicted in a Reuters poll. That headline number was affected by the services PMI, which dropped to a nine-month low, although it remained in growth territory. With customers staying home, growth in demand for services almost dried up. The new business index sank to its lowest reading since April last year just before …