I was looking into the Alan Turing and his Turing test as he proposed and reading some books. I feel skeptical regarding the fact that we have even reached at the level of Artificial Intelligence. It feels like we have not created a Turing machine yet.


a turing machine is a theoretical device that can perform any computation. a language model is a set of matrix multiplications that takes a list of words and gives back the statistically most likely next word.
your question is like asking if novels have become language.
is AI novel or language?
sorry i should have expanded on that:
turing machines are conceptual, like language. they are a theoretical means to formalise and generalise an idea (meaningful computation/communication).
language models are real, like novels. they are one possible use of the concept (word prediction/telling a story).
a novel is a specific implementation of some parts of the idea of language, like a language model is a specific implementation of some parts of the idea of computation embodied by the turing machine concept.