They bought Varyag as a training carrier to get experience with carrier ops, repair and construction. It was never going to be an operationally-deployed carrier.
Their *real* carrier is the Type 001A. They currently have one being worked up and to be commissioned later this year with several more in the pipeline.
Was it not the sister ship to the Admiral Kuznetsov? I know that POS is still looking for a new dry dock to fix damage done to it by a crane. Both these floating follies were built in the late 1980’s so they are antiques. We should not underestimate the Chinese though, they are as perserverant a race as can be found. Why we do anything that helps them build their military amazes me.