LONDON—Euro zone business activity accelerated last month but the bounce may be temporary as demand growth weakened and fears about the Omicron coronavirus variant put a dent in optimism, a survey showed on Friday. IHS Markit’s Flash Composite Purchasing Managers’ Index (PMI), a good gauge of overall economic health, jumped to 55.4 in November from 54.2 in October, below an earlier 55.8 “flash” estimate but still above the 50 mark separating growth from contraction. “An improvement in the rate of economic growth signaled by the euro zone PMI looks likely to be short-lived,” said Chris Williamson, a chief business economist at IHS Markit. “Not only did demand growth weaken, but firms’ expectations of future growth also sank lower as worries about the pandemic intensified again.” The new business index dropped to 54.7 from 55.1, its lowest reading since April. A final PMI for the bloc’s dominant service industry did rise …