I'm a new Manager myself who recently got a new boss. My old boss is still within the company but moved to another department.
This new Manager is quite special: micro manager, asks his team to do things that go against what we've learnt even if we provide proof of it not working, and recently, has been using feedback we give generally to pit us against each other. In my instance, to faciliate his integration since he can be pushy, I offered feedback based on interactions I saw between him and other team members. What I observed was mine but my Manager went on a witchhunt to find out who possibly gave me their feedback, mentioning my name and challenging them about their feedback. My professional integrity took a hit since colleagues thought I went to gossip when I didn't do that.
The Manager is also using feedback I gave about where I thought the department could improve upon being asked the question, to tell others that I have been directly complaining about my ex boss.
I am unsure about how to approach this while my reputation takes a hit.