Staying within a relationship that's unhappy and toxic is always worse than leaving, in my experience.
If ctb attempts are largely the product of emotional instability (speaking from experience, I have BPD) as a reaction to how he treats you, then the relationship is not healthy for you. With BPD, I also struggle (or did a lot when I was younger) with codependency so I wouldn't leave no matter how bad or abusive something was, but staying added more trauma.
You can't change another person. You can only change how accessible you are to that person, and how you react/respond to them.
If you've already sat down and communicated the things that hurt you or trigger you and you're seeing no change, then it's unlikely anything you say or do will force that change.
On the flip side, again speaking from experience, and not at all negating the validity of your emotions and your suicide attempts - but you can't use the attempts as a tool to guilt or manipulate someone into loving / treating you better. It doesn't work. They stay through obligation or fear, not love, and eventually it causes resentment and they leave anyway.
I don't mean that you are deliberately or consciously trying to guilt/manipulate your partner either. You just want it to get better. But you shouldn't have to force someone to treat you well: they should just do it. If they don't, walk away.
Decades ago, first time I fell in love, or what I thought then was love, I was the other woman. Promises to leave and be with me etc etc, which were bullshit… but that's not my point here. Everytime I got hurt over something, I self harmed as a coping mechanism, wanted to kill myself, tried to kill myself - then, I'd say "see, look how much you hurt me, look what you made me do, I love you, why do you keep hurting me?" And he was so scared I'd kill myself, he'd appease me "I'm sorry, I do love you, it'll be better, give me time, stay with me, don't die". Then… no change. Lather rinse repeat.
Truth is, he didn't "make" me do anything. I just couldn't deal with my emotions and that was how I coped. Sure, he treated me bad, but I let him because I was terrified he'd leave me and treating me like shit was somehow better to me than being alone. I repeated similar cycles in my first 3 relationships, til I identified the pattern and then tried to break it. Because there were things I needed to change too, and that involved working on boundaries and self worth.
It's easier said than done, doesn't happen overnight. And if being alone is a trigger, it's hard to leave too.
End of day you're left with a choice: stay and accept how things are, or leave. Neither choice is necessarily what you want, and both will hurt.
I'm sorry everything is so hard for you right now. I hope things get better for whatever path you choose.