No. They are not far behind.
Most navies don’t operate carriers and developing carrier operations, even with Western (US!) help is very, very difficult.
This is an amazing and scary achievement on the PLAN. Think about it. The only other folks operating fleet carriers (not helicopter / VSTOL carriers) are the US, France, and India.
Hopefully, in the event of war, the Liaoning will make for a very happy submarine driver.
All they needed to learn they learned at the knee of Clinton who gave/sold them full access to all things naval including carrier ops.