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The best fight is the one you can walk away from, but you aren't in that position, so now you have to make him tap out. And he has a reputation that can be mobilized against him.

Engage with the rest of your team in 1:1s - intentionally strategize to keep him in the dark, perpetually behind the ball, and mysteriously uninvited from meetings. When he asks questions you say you don't know. When he tries to push an agenda in meetings, you allude to decisions floated in 1:1s he was not there for. This is pure office politics but it will gradually lead to his self-destruction. The org has already demonstrated that it does not care, and this means it is more likely to punish for action than for inaction on your part. Shunning starves him of his best mechanism for toxicity: turning information into vulnerability. He will start acting out when deprived of info. That just means you are winning.