Does Buddhism belong to the traditional culture of China?

Confucianism, Buddhism and Taoism are the foundation of China culture. Buddhism is of course the traditional culture of China. Moreover, Zen Buddhism was born and developed in China, and Tantric Buddhism was born and developed in China and Tibet, so Buddhism is the traditional culture of China, no doubt.

In addition, Buddha Sakyamuni, born in Nepal, first preached in Nepal, India and southern China (now occupied by India). From this perspective, China is also one of the hometowns of Buddhism, and Buddhism itself is the traditional culture of China.