I'm aware of the Batch 3 entering into the serial production but not sure about the Batch 4 though
According to a May 2021 report by The Diplomat, some 50 units of the jet are currently in operation. The J-15 is China's first carrier-borne fighter jet, meaning that it was primarily designed for China's growing fleet of aircraft carriers
Take a look at the J-15 fighter jet, the $61 million copy of a Soviet plane picked to wage war from China's aircraft carriers | Business Insider India
Chinese J-15 fighter jets on the deck of the Liaoning aircraft carrier during military drills in the Yellow Sea, off China's east coast.Contributor/AFP/STR/China OUT/Getty ImagesChina's touts the J-15 as its first locally made carrier-borne fighter jet.The jet is an unlicensed copy of a...www.businessinsider.in
That 003 China aircraft carrier is suppose to defend the Taiwan strait., not used as an offensive weapon to project power half way across the world like American warships. It would have been too risky to develop a whole new generation of engine plus catapult system plus new layout all in one go so this step by step approach was the safer bet