The ROK government has not recognized Taiwan as a state since the 90s because of China’s influence. However, the two countries operate in the same circles because they are both tied to the US on military affairs. Taiwan is not an ally but a partner of the US’ hub-and-spokes alliance system (which ROK is a part of) in the Pacific and rightfully so because of Taiwan’s important geopolitical position and because the US and its allies must hedge against China’s growing influence. So, even though Korea doesn’t even have diplomatic relations with Taiwan, they are on the same side when it comes to military affairs. ROK will never recognize Taiwan (like many other countries) because they need to work with China on bigger issues.