They've been very inconsistent about the concept of spoiling the story. They're not gonna remaster Dirge because it will spoil the ending, but CC's fine, which reveals the central twist of the OG? Okay, lol.
Now, from my perspective, this game is 25 years old. The spoilers are plainly out there, there's not much sense in trying to maintain the secrets outside the game. Anyone who got into the Remake fresh and visits an FF reddit or wiki is going to learn everything about Zack anyway. But as I've argued in the discussions about Aerith dying or not dying - at it's core, the impact of the story was in the satisfying way it's told, not the mere "shock" of it. In having us spend more meaningful time with Aerith, and seeing more of her as a person, they have already made the impact of that hypothetical moment harder, even without the surprise. Similarly, the truth of Cloud's past would be every bit as satisfying to behold with the improvements in storytelling and character interaction, even though we already know what's going to happen.
Now, obviously, they have made it very clear that they are not catering to my perspective. So the real answer is probably, as you imply, that the mystery of Cloud's past will not be mystery for long, because we've got a Zack-shaped shoehorn hovering over the game like the sword of Damocles. So if we're gonna mash him into the plot like strawberry preserves, it's more useful that the new audience knows who Zack is than that they don't know about the twist about who Cloud is.