Do we need to break up, or am I giving up?

I (29F) and my partner (30M) are both are difficult points in our mental health journeys, I have BPD and he has depression. I was already struggling with my mental health and my partner cut contact with me for a month because he wasn’t confident in my ability to support him with his mental health crisis. While this made me angry because it felt like an abandonment, I understood that he did what he had to do. We reinstated contact about a week ago, then due to a miscommunication which made him spiral, he cut contact again as and his best friend told me that if he were to end his life, it would be on me.

The last contact we had (combined with other stressful events in my life) have made me spiral and enter further into a crisis, to the point where I can’t be alone due to concerns around my safety and my care team in mental health services are trying to avoid about a hospital admission.

However, my time alone has let me reflect a lot. There are definitely aspects of the relationship that are problematic and I feel like the way our individual mental health impacts each other only makes us hurt each other more, nothing I do is with bad intentions but he is so sensitive to rejection that it hurts him badly, it makes me feel like I’m a failure and makes the aspects of having BPD so much harder to handle. It’s dawning on me that our relationship currently isn’t healthy and I’m wondering whether breaking up is a sensible option, or whether I’m running away? I’m finding it hard to think of the right decision as I’m unwell myself. It’s very difficult because I love him so much and could otherwise see a future with him but I want to do the right thing for him and myself.

Any guidance would be much appreciated.