I don't recall them saying she died in any of the movie's explanations/flashbacks, just that she was captured and imprisoned.
I suppose it's possible that she was killed because something/someone had changed events before Logan, but since I don't recall any actual mention of her death, what's to say they couldn't have simply kept her alive during their research of her DNA allowing for Magneto to eventually find and free her and thus allowing her to be present for the original 3 movies... But since they essentially hit the massive restart button on the franchise, that's all moot point now anyways, isn't it?
Trask himself says he wanted a lot of tissue samples from Mystique, including brain tissue. And he had a history of killing the mutants he experimented on. But its possible in the original timeline where he was killed that the scientists that continued his research were more cautious, not wanting to kill the golden goose, and kept her alive. Eventually, we know Magneto himself escapes confinement (because he also is free in the 90s at the time of the first X-Men movie) and with Magneto on the loose, its possible he somehow managed to break Mystique free as well.
There is the question of why Magneto allowed the Sentinel research to continue; if he manages to free Mystique at some point then its likely he knew she was being held by scientists. But its possible he didn't know what their research was about, and didn't care at that time - he might have thought it was base experimentation of the kind he himself suffered in the past. In fact, there's a subtle (unintentional) hint that Magneto *did* know at least some of what was going on. In X2 Magneto is shown to be aware of William Stryker and at least moderately familiar with some of his activities. Perhaps when Trask died in the original timeline its Stryker that initially continues working with Trask Industries, before eventually branching out on his own when he decides that the Trask goal of creating adaptive robotic Sentinels - a task that is taking decades - is not the answer, and he decides to form the Weapon X project. There's a certain logic to Magneto freeing Mystique from Trask Industries when Stryker was still there and thus aware of his proclivities. When Stryker's research facility was destroyed and Stryker himself (probably) courtmartialed from the military at the end of X-Men Origins: Wolverine, Magneto probably thought he'd heard the last of him.
