China's underlying logic in the SCS shares similarities with the Monroe Doctrine in the Caribbean. It is not likely that China would claim the whole sea as 100% sovereign waters. I think China is trying to make a grand bargain in the region that results in it being the preeminent power of the region and other nations would be compelled to join a China lead regional order (Japan, Korea, Vietnam, Philippines, Singapore). There would be free navigation and exploration of resources by other nations, just under a different framework. Ultimately China views the current framework an architecture that it didn't participate in creating thus would like to contribute its "ideas".
Give a listen to Michael Pillsbury's videos or read his books, it provides some good insight into the overall picture. I've bought his book "The Hundred Year Marathon". He outlines the perspectives of some in China's government quite well as he speaks Mandarin, reads Chinese and had experience dealing with Chinese officials and military officers. I encourage more young people to learn Mandarin and be able to read Chinese as the language barrier is a big disadvantage for the West in understanding China.
Noting that today's PRC's vision for the geopolitical order in East Asia closely corresponds to an updated version of the actual geopolitical order in East Asia for much of history, updated mostly according to international agreements which have not been fully honored by others particularly the US and Japan. And given the as yet unresolved Chinese civil war between the PRC and RoC.