For manslaughter to apply, she doesn’t have to discharge the weapon accidentally, but rather, recklessly. Like if she peaked around the corner, heard a noise in the dark and fired blindly into the room resulting in Jean’s death.
For murder, her actions need to be intentional, which they seem to have been. She intended to shoot the person who stood before her.
Legally, if she goes to trial, she might be in a better position if she is charged with murder because then she has a better defense. She can argue “mistake of fact” and basically say that she mistakenly believed an intruder had unlawfully entered her home intending to cause her harm (physical or financial) and she shot him in self defense, rightfully, under the Castle Doctrine.
If the jury believes she truly thought it was her apartment and Jean was a burglar, they could acquit her. Charging her with manslaughter basically denies her this defense, but puts her in a better position if she pleads guilty.