Did Fujian Road include Taiwan Province Island in Song Dynasty?

Taiwan Province Province was formally incorporated into the unified territory in the Yuan Dynasty, and the Penghu Inspection Department established by the Yuan government was the first government agency in the history of China to formally manage Taiwan Province Province and its affiliated islands.

The high school history textbook clearly says ~

There is no doubt about it.

As for the original Baidu Encyclopedia you mentioned: The written history of Taiwan Province Province can be traced back to 230 AD. At that time, King Sun Quan of the Three Kingdoms sent 1000 officers and men to Yizhou (Taiwan Province Province), and Kuloko Shen of the State of Wu wrote the earliest account of Taiwan Province Province in the world. During the Sui and Tang Dynasties (AD 589-6 18), Taiwan Province Province was called "Liuqiu". The Sui Dynasty worked as a teacher in Taiwan Province Province for three times. According to historical records, in 6 10 A.D. (the sixth year of Sui Daye), Han people began to migrate to Penghu. By the Song and Yuan Dynasties (AD 960- 1368), there had been a considerable number of Han people in Penghu. After the Han people opened Penghu, they began to develop in Taiwan Province Province, bringing advanced production technology at that time. /kloc-In the middle of the 0/2nd century, the Song Dynasty placed Penghu under the jurisdiction of Jinjiang County, Quanzhou, Fujian Province, and sent troops to defend it. The Yuan Dynasty also sent troops to Taiwan Province Province. The Yuan and Ming governments set up a patrol inspection department in Penghu, which was responsible for patrolling criminals and holding salt classes. In the late Ming Dynasty, the scale of development became larger and larger. In the era of war and famine, the Fujian authorities of the Ming government and Zheng Zhilong Group immigrated to Taiwan Province Province in an organized way.

Pay attention to this sentence:/kloc-In the middle of the 2nd century, the Song Dynasty placed Penghu under the jurisdiction of Jinjiang County, Quanzhou, Fujian Province, and sent troops to guard it.

It's Penghu Islands, not Taiwan Province Province.

Taiwan Province Island was officially managed by the Yuan Dynasty.