OP, you may find the following post by Zawn Villines on the weaponizing of suicide threats by abusive partners useful. Your H is not threatening suicide but his self-harming acts are akin to it. Here are some snippets, I recommend to read the piece in whole:
"Abuse is fundamentally about control. And one of the most powerful ways to control someone who loves you is to threaten your own death. This is why abusers, especially abusive men, may weaponize their mental health, threatening suicide when they sense they are losing control...
If your partner threatens suicide every time you try to leave, or even every time you demand that he do a fair share of household labor, you are not alone. You are not the problem, and you’re not the abusive one...
Why abusers so often threaten suicide
Abusers may threaten suicide for a myriad of reasons. Sometimes, they have no intention of following through with the threat, and are wielding it as a deliberate and conscious act of control.
More often, though, they really are feeling suicidal. People who engage in abusive behavior have refused to learn how to safely manage their own emotions. So instead, they control their emotions by controlling others, and often by making others responsible for the abuser’s feelings.
When your abuser can’t control you, or finds their emotions overwhelming, they may feel hopeless. Remember, after all, that some portion of their identity and sense of worth comes from controlling you.
Abuse survivors often interpret an abuser’s suicide threats as a sign that the abuser is the victim, and that they need to lay off—by, for example, requesting less household labor. In reality, suicide threats from an abuser signal that he is either totally out of control or dangerously manipulative. ...
The dynamics of suicide threats—and why they can be so effective
Men who threaten suicide to get what they want are asking women to make a simple choice: your life or his. And patriarchy tells women we must always choose the man’s life over ours. It tells us we’re abusive monsters for even considering our well-being over his.
Suicide threats don’t have to be overt to work. I’ve spoken to hundreds of women who avoid taking certain actions—calling CPS or the police, divorcing their abusers, telling their husbands no, declining sex—because they fear their abusers may become suicidal...
It doesn’t matter whether he is genuinely suicidal or not. When he wields the threat to convince you to stay, talk to him, have sex with him, or otherwise give him what he wants, he is being abusive...
All threats of suicide are serious threats, even if he has a history of manipulation.
This is because there is simply no way to distinguish an earnest threat from an attempt at manipulation.
If he is earnest in his intentions, then he needs help you cannot give him. And he deserves that help, because everyone deserves a chance at redemption and healing. Ensuring he gets that help is an act of decency, not cruelty.
And if he is being manipulative, he’s much less likely to continue wielding this threat if you take it seriously and he has to answer to someone else about his behavior.
Call for emergency help every single time he threatens suicide. Document the threat. Continue to push for treatment and call emergency services.
Every. Single. Time.
A threat of suicide is not something you can fix for him, and the most loving and self-protective thing you can do is get him expert help."
zawn.substack.com/p/when-your-abuser-threatens-suicide