In the matter of threatening suicide people that are serious about suicide will find ways to carry out their choice regardless of how vigilant you are.
While you are not responsible for any action she might take we are all responsible for not giving reason for them to promote the idea through our behaviour. Once we are satisfied that we are being fair, reasonable and so on and we want to separate then beyond that we cant be held responsible.
Those that threaten suicide imo need to be evaluated by professional medical people so you can recommend they see a doctor, even offer to accompany her. But your plans to separate should not be left on hold for very long after you have announced them because if you do she will assume that is the way she will accomplish her plan- emotional blackmail.
So be careful, fair, reasonable, firm and supportive but not bend to accommodate her threats.
When she states "you don't care" say to yourself "I know I do care, her assessment of my level of care is her perspective...it is wrong but I am not here to convince her, she is entitled to her own opinion".
There are a lot of narcissistic people around. If she hasn't been diagnosed you cant label her as such, however, like the last paragraph, you have a right to an opinion. Her comments that say "its all your fault" are very common in arguments, turning around accusations is a handy tool for some. However your own mental strength if waning, will display you weak minded and question yourself. That could well be a weakness she is aware of and using that weakness is a sign I would not call love.
Don't be afraid of yourself being weak minded. We cant all be strong in every regard. But we also should not take criticism for what is natural.
I hope I've helped you clarify any need for medical assessment and moving forward a visit to your GP would be beneficial with or without her.