The point of the Turing Test is that if there is no extrinsic difference between a human and a machine the intrinsic difference is moot for practical purposes. That is not an argument to whether a machine (with linear algebra, machine learning, large language models, or any other method) can think or what constitutes thinking or consciousness.
The Chinese Room thought experiment is a compliment on the intrinsic side of the comparison: https://en.wikipedia.org/wiki/Chinese_room