I can say conclusively that I have dealt with "cyclothymic disorder," and while understanding it, things did not end well.
If you have to be there, start looking around for a different situation.
In the meantime, work on building up allies with others and document all of your observations.
By documentation, I mean do something like send yourself an email in the companies email system every time you have an interaction or observe something or hear something. This is an ongoing record you can point to if you need to.
Any time this person has a work related interaction involving you, but it is not written down, write it down. In an email, in a ticket, on a wiki/confluence page. "Today Bob, Sandra and I talked about X and decided to do Y". State who was involved in the discussion, what was decided, who said what. This is good practice for capturing any of these ad-hoc interactions at work, so make a habit of it.
If this person attempts to gaslight you (likely) you can refer back to what you wrote down.
How can this be done?
The best way to handle it is to not be there.
The second best way to handle it is to not be there.