Blinken ruffles feathers by stating US ‘does not support Taiwan independence’ after meeting China’s Xi

That's a simple statement of current US policy. The US supports the status quo of limited independence of Taiwan under the government of China.

Mainly it's an attempt to not have to fight with China about technologies that are manufactured in Taiwan, while still keeping global access to that tech. As the US and other countries invest heavily in chip manufacturing though, it will become less and less important that Taiwan stay independent.