I think the bigger question is if this is mostly for a Chinese audience why do they need to mention the event everywhere? How long do they need to keep self flagellating until they have made penance and will be forgiven for whatever transgressions occurred?
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Search for 六四政治风波 (4th of June political disturbances) rather than searching 天安门事件 (Tiananmen Incident). You'll find high level references to the political situation at the time.
Here is a (once again high level) Party summary of the circumstances surrounding the event, and some actions taken including the clearing of Tiananmen square on the morning of the 4th of June.
Articles I turn up since then appear to simply repudiate the USA's position on the events without further substantiating China's own. This is perhaps an oversight on China's behalf to 'set the record straight' with readily accessible information online. I hope you turn up more information in your research.
Adding to RoomAndBored's comment
https://lemmygrad.ml/comment/460227
Even a quick search of this term in Baidu will bring up results with the term 政治风波.
Here is ProleWiki’s article.
It might not be mentioned because, although there were protests in the square, all deaths were in streets near the square instead of in the square itself.
It's probably censored because it's a politically sensitive topic. From my reading, the article is meant to promote tourism and pride in national monuments, not to discuss history in detail. Mentioning those events is seen as encouraging social unrest.
How about this, why doesn't it mention the October 28th 2013 terrorist attack? https://baike.baidu.com/item/10%C2%B728%E6%9A%B4%E5%8A%9B%E6%81%90%E6%80%96%E8%A2%AD%E5%87%BB%E6%A1%88/12022667
On 1989 Political Disturbance: https://lemmygrad.ml/post/1252700