The British estimate (declassified in 2017) agreed with the American intelligence estimate (over 10,000 dead and 40,000 wounded) that was released in 2014.
The British released a lot of details on how the attack was carried out, including the use of promises (quickly broken) to allow demonstrators (including survivors of the first round of killing) to leave. The troops apparently had orders to kill all civilians in the square and destroy the bodies where they fell. This included crushing the dead using armored vehicles, burning those remains and flushing those remains down storm drains. The area was sealed off for over a month so the cleanup could be thorough.
The Chinese government publicly says 300 died. Privately they say over 10,000 died, apparently.
But it worked. The shock of mass slaughter killed the impulse for democracy in China for the last 30 years. Or at least killed the potential leaders who might argue for democracy and organize the discontented Chinese who see the lack of freedom and the corruption that allows party members to live very well indeed.
The Chinese followed up with arrests and to this day still clamp down censorship on the anniversary.
Eventually the effects of such a mass killing wear off. The Elder Assad slaughtered civilians with an army assault on Hama in 1982 that kept their rule in Syria intact. Twenty-nine years later, in 2011, protests erupted that developed into a rebellion and then a multi-war as factions multiplied and foreign states and non-state entities entered the fray.
This June will be the 29th anniversary of Tiananman Square, coincidentally enough.
Obviously, I'm not saying Syria provides a template or timeline to predict China. But eventually the effects of a mass killing wear off.
And China's rulers do worry that they sit on top a mass of potentially revolutionary people who could be set off by a spark nobody sees coming.
Let's just hope China doesn't see a short and glorious foreign war as the tool to rally Chinese around the government. (Unless the target is North Korea. Hmmm.)