As my dear friend (Roger Waters) would say “Run like Hell”.

RUN!!

You'll make the world a better place! Don't marry her!

Here is another ultimatum for her: call the cops, have her taken to the hospital, inform a head doctor of her ultimatum she gave you, proceed with a restraining order and leave her. If she's "bluffing" then that suggestion will possibly scare her into not doing anything stupid if she doesn't want a record on her mental state and problems from the authorities. Still leave her regardless as that is a red flag for three weeks into the relationship. If she isn't bluffing, you will be making sure she receives some help before leaving her behind. Either way, you're better off leaving that crazy woman behind OP.

Threatening suicide to get someone to do something is actually domestic violence. Anyway, it sounds like she has BPD. Take the threat seriously and recommend she get help.

Call the police bro. Suicide is illegal and she threatened you. They'll arrest her and do a mental evaluation on her and all that

Highly unlikely that she'd actually do her self in, but on the off chance she's batshit crazy...I'd tell her "we need to see a marriage counselor before we get married to make sure it's gonna work"...then explain to the counselor her threat...maybe they can get her the help she needs & you can run far & fast in the opposite direction

Run.

So, when is the wedding?

If she really wanted to die, even that wouldn't keep her from doing it.