This is not a former relationship issue. During the Qing dynasty China didn’t really care about rugged distant Formosa, and initial modern development happened under the Japanese. So the historical claim is hollow. What is important is that Taiwan is in the center of the first island chain running from Japan to the Philippines, and blocking China's unrestricted access to the Pacific. They need that geopolitical location to expand their new empirical influence, the culture and history angle is just PR window-dressing.