There are a few errors in the premise you give. I'll address those since I think in doing so it will address your question. If there are follow ups about the historical context, well I just decided to not apply to that job in Beijing after all, so I'll be happy to answer those as they come.

First, they didn't keep it secret. The protests were a national thing, not just happening in Tiananmen, and the crackdown was known throughout the country when it happened. There wasn't just one reason people were protesting. May 4th style democratic reforms was one reason, but protests happened across the country in every major city, and when it was shut down in Beijing, obviously people heard about it. Protests continued in places like Nanjing even after the crackdown.

Second, it's not true that people don't know about it in China. People very much know. Instead what is happening is a few things:

• They're not going to talk about it openly because there are still real consequences for doing so, even if those consequences for many people are simply social in nature (i.e. I could bring it up with friends and not worry about the cops showing up, but the friends may respond poorly and it can cost me those relationships.)

• In hind-sight people think the protestors were in the wrong and the government action, while harsh, was justified. (Note this isn't me saying this so don't jump down my throat as an apologist for Deng Xiaoping. I have a formal record with my local Party secretary showing quite the opposite. I'm just saying what some people's positions are)

• People don't actually think the protestors were in the wrong, but it's simple self-preservation to say sure, that's the situation.

• They're not going to talk about it with a foreigner, even if you are good friends. I can beat up my kid brother but god help you if you think you can pick on him. That sort of thing. Context matters.

Moving on,

I find it very hard that the government would be able to deny such a large and public event.

I'm not sure why this seems unreasonable or difficult. And anyway they don't deny that anything happened. They just don't allow continued picking at it.

Does the Chinese population actually not know about the event ...

Everyone knows. Millennials and Gen Z folks tend not to care as it was in the past, China's doing fine now, why are you hung up on the past etc etc etc. Gen X types know but know better than to go around shouting about it, for their own well-being. People overseas talk about it pretty openly though, as well as in Hong Kong with an annual commemoration, photos of which you'll surely see in a couple days.

or is it an open secret amongst everyone ...

That's the answer.

or is it seen as a kind of conspiracy theory that some believe and others deny happened?

Not aware of anyone who straight up thinks it's a conspiracy. Maybe some people think this but it's not a widespread popular position. In all my adult life I've not once heard this as someone's take. It's much more common to say it happened and it sucked but it was the right thing to do so let's not dwell.

Hope that helps. Again, to be clear, this isn't me saying it was good or they deserved it, just that that's what some feel. So please don't attack me for having that position myself, which I do not.