Most time travel in Trek seems to result in retroactive bootstrap paradoxes. History is only theoretical until it is directly observed, with many possible histories converging onto the present, and the observation of a time traveler collapses the waveform for them into a version of history where they were integral to events.
Before La’an went back, things played out how they played out. After she inserted herself into the timeline, events changed, but the outcomes of relatively minor changes like the gun were already anchored in the future, and so they didn’t significantly alter the final outcome. The path may have changed, but the destination remained the same.