SHANGHAI—In the search for new growth in the world’s biggest internet market, China’s three tech titans are spending billions of dollars on dozens of fronts to find the next big thing.

The latest battleground is China’s lifestyle trends, with companies investing in apps that offer a variety of services including food, face-lifts, child care and bike sharing. E-commerce giant Alibaba Group Holding Ltd., social-media champion Tencent Holdings Ltd. and search engine Baidu Inc. are betting that one-stop shops that match merchants...