I think it is just missunderstanding here. UNESCO website explain everything you need to know, therefore there is nothing to worry:
Indonesian batik was added to UNESCO’s Intangible
Cultural Heritage of Humanity list in 2009, and has been internationally recognized as an historical fabric of human civilization. It is thought to be over 1000 years old, with historical evidence pointing to its use in parts of Africa, Asia, and the Middle East. Although the actual
origins of batik are unknown, it is believed to have been transported to Asia by way of the Indian subcontinent. “
Batik” is derived from an Indonesian-malay word, which is
now often used as a generic term referring to the process of dyeing fabric.
https://en.unesco.org/silkroad/content/cultural-selection-batik-world-exhibition-unesco
First, the status that UNESCO give about batik to Indonesia is the "heritage status", not the "origin".
The reason why Unesco give Indonesian batik a heritage of humanity status, could be because of popularity, not because the origin.
Second, UNESCO admit that the origin of Batik is unknown, and mention other older civilization (Egypt, China, India, Africa) to have used this technique (Batik) before that.
Third, Batik although it is Indonesian/Malay word,
now it become generic word.
So I think there is nothing wrong for Xinhua to say: Batik is a traditional craft common among ethnic groups in China, as it is historical and factual; not wrong because they don't claim it originated from China; and we Indonesian doesn't need to worry as the Xinhua's claim/statement doesn't dent the "cultural heritage of humanity" status that UNESCO has given to Indonesian Batik in 2019.
Origin (unknown), tradition (Egypt, China, India, Indonesia), and cultural heritage to humanity status (Indonesian Batik) are 3 different things that not necessarily contradict among them.