This is no different than a chemical plant "accidentally" building a conduit a quarter mile and dumping waste into a river. Of course they know.
However I have made mistakes like that programming all the time... for example, having massively more data written out to disk than I had intended. You are never going to make a mistake in a factory that increases its electricity consumption by 1,000,000x but I have made errors that caused a million times more data to be written out to disk than planned.
Maybe not a million, but a thousand times? Sure. Just short some heavy machinery and watch the amperes light up the day like a second sun as they rush out to pour into the ground. Factories have breakers to prevent that, you'll say. Turns out software projects don't have fuse equivalents, even though they should. The reason is that bleeding electricity is expensive (and dangerous to people, which from the company's POV means "even more expensive"), whereas data leaks aren't. I hope the latter is going to change.
Recently I read an article saying that programmers should reserve "error" for the mathematical usage of "distance from correct result" (as in, behavior of the program), and refer to their bugs and other mistakes as "blunders" instead. I have to think on it more but I like the overall direction of the distinction.
If you step into the street in front of a truck because you think the truck is farther away than it turns out to be, it's an error. If you are playing baseball, and you estimate the vector to intercept a ball rolling along, and you touch your glove to the ball but fail to actually catch it, it will be classified as an error, You made an estimate of what the circumstances were, and it was wrong and you acted on purpose.
Likewise their definition of mistake uses error a couple of times. https://www.dictionary.com/browse/mistake
I get it though, there is a subtle difference. I'm just saying both terms mischaracterize (intentionally) what I think was likely a very intentional, knowing and calculated action by Twitter. I'm asserting without proof that there was no inattention as in your first example, and no miscalculation as in your second example.
The baseball example is problematic because "error" has a game-specific meaning just like "run" and "base," and whether you commit a mistake or an error, they will both be recorded as errors.