What was the track of China culture spreading eastward during the Japanese Asuka period?

In the most advanced areas at that time, such as the flying bird where the palace was located at that time, Takashi in Nara Prefecture, Nanbo outside Dahe County, that is, Motomachi in Tianwangsi District of Osaka Prefecture, the flying bird culture centered on Buddhism became increasingly prosperous. As the name implies, the bird culture is named after the Asuka period. With regard to the spread of China culture to the East, we cannot but mention the Korean Peninsula. Through the archaeological excavation of Faxing Temple, it is confirmed that the Korean Peninsula played an intermediary role in the process of Buddhism spreading from China to Japan. The China culture introduced into Japan from Asuka period was mainly Buddhism, and there were three main paths.

1. The Buddhist culture of the Northern Wei Dynasty located in the northern part of the mainland was introduced into the Japanese archipelago through Koguryo. In fact, the Buddha statues carved by Zhili Giant Buddha, such as the flying bird Buddha in Faxing Temple, the three pharmacists in Horyuji and the three Buddha statues of Sakyamuni, all have the hard-core style of Gu Zhuo.

2. It is the Buddhist culture of the Northern Qi and Northern Zhou Dynasties (Southern Dynasties) located in the central part of the mainland. It was introduced to the Japanese archipelago through Baekje and Silla, represented by Maitreya statues in Guanglong Temple and Zhonggong Temple, with a rational and soft style.

3. Later, it was introduced directly from the unified Sui Dynasty in China. Represented by the Guanyin Bodhisattva statue in Guo Yicheng Temple and the Holy Guanyin statue in Helin Temple, the Buddha statues at that time revealed an implicit style.

I don't know if I understand the meaning of your question correctly.