Surprising there is no English language translation of the Chinese update 10th June, despite it basically being no information:
民航局介绍“3·21”东航MU5735航空器飞行事故最新进展 (yicai.com)
At the meeting, Dong Zhiyi, deputy director of the Civil Aviation Administration of China, said that after the "3.21" China Eastern Airlines MU5735 aircraft flight accident, in accordance with the relevant laws and regulations of China and the relevant provisions of the Convention on International Civil Aviation, the Civil Aviation Administration of China launched the technical investigation of the accident, and on April 20, the preliminary report and information circular of the accident investigation were announced to the public. At present, the accident investigation department is strictly following the investigation procedures and is still continuing to carry out in-depth wreckage and data evidence inspection, flight data analysis, experimental verification and other related work. Subsequently, with the advancement of the investigation work, the Civil Aviation Administration will release the progress and relevant information of the technical investigation of the accident in a timely and accurate manner in accordance with laws and regulations. - Google Translate