At that moment, did some part of her die, or was a part of her reborn, I wonder?
Both. Death is the Mizu that could have been: loving if submissive housewife with revenge slowly eroding at the wayside. Rebirth is the ouryo that has became Mizu after she came to the conclusion of Mikio or her mother selling her out and leaving her at alone against bounty hunters, moreso the former as she's betrayed by the man she came to love at that point.Revenge is always there but it was half hearted considering she just went ans demanding info from opium traders in spite of her blue eyes fully exposed and getting stabbed for it. Once she's become the agent of revengeance, Mizu solidified her will by throwing away any notion of happiness she could achieve and instead be walking demon of hate, revenge and disaster.