I'm so sorry about all you are going through, but I see you are a strong woman with a good sense of self-preservation for yourself and your son. Good for you. Your story sounds similar to mine in many ways.
When his anxiety and depression got worse he latched onto the OW as she made him "feel better" and "she understood him."
I was married for more than 25 years when I learned my husband wasn't who I thought he was (turned out he was a SA among other things with multiple betrayals.) He voluntarily entered inpatient treatment to the tune of $60,000, then lied to them for more than half his time there (until I found some things in his google history and he was afraid I'd let them know so he told them) Anyhow, the point of all this is twofold. 1) Try to remember his actions, not his words or promises. And, 2) my ex was diagnosed with Borderline Personality Disorder and Narcissistic Traits. A lot of what you are sharing about your H sounds like BPD - the cutting, the self harm, the looking to others for a sense of self. (The book Walking on Eggshells is a good resource) The lack of remorse and blaming others like the children for their unhappiness sounds like narcissism. (Dr. Ramani has great videos). Unfortunately, neither of those things are really fixable. Borderlines can learn coping tools through DBT therapy, but they will always be broken to some degree. Narcissists are who they are.
Someone in an earlier post mentioned boys needing their fathers. I'd argue that boys need healthy male role models, and it sounds like there are others in your family who may be able to offer that better than your H. That's not to cut him off completely, but good boundaries and supervision will be key.
I moved in two steps. First I filed for legal separation because I wanted to protect my assets and our daughter's future and I didn't know if my ex would be sued by his gf (an employee). Then, after a false attempt at R, I divorced.
It looks like the law in NC would allow you to take a similar path. You can quickly obtain a legal separation, and then a year from now convert that to a divorce. You also have the option of suing the OW.
Although adultery is not a ground for an absolute divorce, it is a ground for legal separation, called "divorce from bed and board" in North Carolina. If your spouse has cheated, and you'd like to legally separate from your spouse without ending your marriage, you can request a divorce from bed and board, using adultery as the grounds for your request. (N.C. Gen. Stat. § 50-7.)
In North Carolina, the most common ground for divorce is based on a separation for at least one year. So long as the couple lived separate and apart for the full year and did not resume their marriage (or cohabitate) during that year, the court will grant the divorce. You must also be a resident in North Carolina for at least six months before filing for divorce for the court to accept your case. (N.C. Gen. Stat. § 50-6.) While adultery by husband, wife, or both may destroy a marriage, but you can't use it as a ground for your divorce in North Carolina.
North Carolina is one of only a few states that permit a spouse to file a civil lawsuit against the spouse's lover or anyone who interfered with the marriage. Spouses need to file this lawsuit outside the divorce court in the regular civil court system. These lawsuits fall under two categories: "alienation of affection" and "criminal conversation."
Good luck. Please take care of yourself. Find a therapist to help you with your trauma. and do some self care.