TOKYO—Asian shares sank in cautious trading Tuesday following a decline on Wall Street amid continuing worries about the Omicron coronavirus variant, especially rising cases in China. Japan’s benchmark Nikkei 225 fell 0.8 percent in morning trading to 28,242.46. South Korea’s Kospi was little changed at 2,926.01. Australia’s S&P/ASX 200 dipped 0.8 percent to 7,391.50. Hong Kong’s Hang Seng lost 0.5 percent to 23,640.42, while the Shanghai Composite inched down less than 0.1 percent to 3,592.35. Asian markets also have their eyes on the U.S. Federal Reserve, which is expected to tighten interest rates this year. What happens in China is also likely to have regional repercussions. Major companies, including automakers such as Toyota, had been counting on a recovery in the supply of semiconductor chips and other products from China and the rest of Asia. The recent surge in infections by Omicron has thrown a wrench into such hopes. On …