This is my top contender for how conspiracy theories can be real.

I think a good real-world example of this is the mask coverups:

Stage 1. During the initial stage of the COVID-19 pandemic, governments coordinated a lie that masks do not work, despite providing massive amounts of masks to healthcare workers. This was, obviously, done because they wished to prioritise health workers' access to masks.

Stage 2. Governments did an about-face and implied that masks should be worn and any mask - including a home-made cloth mask - would be effective. Some civil society organisations did think this as well, but perhaps this was part of a well-organised psyop campaign, I don't know.

Stage 3. Research came to light showing that there is no evidence that cloth masks (as opposed to N95 masks) work against COVID-19, e.g. the Cochrane Review on this question, but governments did not respond to this or admit their mistake. This suggests that Stage 2 was part of a continuing cover-up designed to protect healthcare workers' access to N95 masks, which were never promoted for use by the public, but IMO should have been.

Will there be a new "embarrassing truth" that's not presently known at the time of writing this question, but which is discovered and governments don't acknowledge because it's too embarassing, but nevertheless is highly significant and they ought to acknowledge?

I will not actively seek out examples of this, so they will need to be posted in the comments. Obviously, in order to resolve as Yes, the provided "embarassing truth" has to actually (a) be proven true by some reliable method (b) be embarassing to governments to an extent where they wouldn't acknowledge it as true, even though it is significant in some way to a large number of voters/citizens. (Tyrannical regimes refusing to acknowledge things does not count, this market covers things that democratic governments refuse to acknowledge.)