How do I move forward after working with a toxic academic supervisor?

I think you will have to be transparent about the relationship in the lab when potential employers ask for that reference. However, assuming you warned whatever graduate degree you had, it can also be taken as a sign that despite a toxic work environment you were able to still carve out success. Everyone has experienced a toxic work environment, so if your story is authentic, and you sound authentic, employers might be able to identify that.

But what you can’t do is use that supervisor as a reference, and you most likely won’t get other faculty to speak poorly about your supervisor in a letter. So, I would argue, that you just need to be transparent about your experience when you need to confront it.