I think unhinged reply is excellent.
Ashamed, when there’s another betrayed partner is only fair to give them the chance to reclaim their stolen agency and decide if the want to live with infidelity or they want out.
I don’t know if your husband has additional goals other than justice and fairness, maybe he’s taking revenge on the Affair Partner who destroyed his life in part, which is correct to say he is irrelevant and worthless, as he has no power over his life besides the power your affair gave him temporarily.
Now he’s harmless to your husband, and his informing OBS is just, if he gets some satisfaction over the AP for what he did it’s also kinda fair, h deserves it.
He might feel a bit better about it and he also might feel some vindication in showing you the AP "lying POS" side, that he denies your existence because you never really mattered to him, you were just free validation in his eyes.
That said, I think the reasons above not to keep contact too close between BSes is very valid.
They can exchange notes and confront the lies between waywards (speculation: if he thinks you didn’t fully come clean and are trickle truing, their exchange of notes may help him to know and save himself from trickle truths, that are as devastating as the affair). They can maybe set a checkpoint in the future.
But they should not be in constant contact. Your boundary here is really making sense. Maybe try to explain to him if he can make it so they do exchange information but it doesn’t become a "relationship " in the sense of colleagues, not romantic. They should heal each other separately and when needed they know they can email each other for help.
No friendship though. They are both still with their waywards, and you might be tempted to contact the AP (or him to contact you) to work out a common story to tell (gentle name for lies, don’t follow it even if tempted, lies will always fall. You risk to sabotage any R if that’s your goal).
You all need space and clarity to heal and find yourself again.
This is fair and may help bs, but it can be a double edged sword and source of triggers if not minimized and very controlled (and their emotional state ain’t the best right now most likely).