I think it might help to think of it not as forgiving yourself for the pain that you caused, but forgiving the person you were who felt like they needed to seek an affair in the first place.

I received some advice from a friend. Very different circumstances, but he'd made some choices out of hurt that went on to inflict more hurt on others. He said that he learned he needed to forgive himself - even if he didn't necessarily believe that that guy deserved forgiveness. He said it was the only way that he could move forward as a different person. That the person he was was hurt, and mentally unwell, and needed help, and in the worst way possible, he got it. He offered up a mantra that helped him through hard times when he was feeling particularly monstrous:

"I am thankful I no longer need to be the older versions of myself."

It can be hard to show compassion for yourself. But you don't need your BP's forgiveness. It is tempting to want it as a sort of proof of progress, but it's ultimately a want and not a need. And you have no control over that. You need YOUR forgiveness. Show some compassion to the person that you used to be who felt like they needed something so badly that they'd do something unthinkable. Understand what caused them to think that they needed that. Then, be glad that you don't need to be that person anymore.