I've found it much easier to "vote with your feet" when it comes to faulty leaders rather than attempt to work around them or risk being labeled "difficult to work with" as from my experience it seems to be related to the manager's ego (assuming your not a dongus and are flagging valid things when necessary).
Within any large company, an internal move is fairly simple stuff and an external move will always be more lucrative in terms of compensation.
I can work around one bad manager. It is when you get 2 or 3 stacked vertically over each other that you know things are not only never going to change, but that top level leader has tanked all other departments underneath them, and it is time to move somewhere else.
I used to not worry about higher level leadership in large companies because I thought I was too low level to really be impacted by them. I no longer think that way, and I look into as much of the leadership as I can before accepting a role.
I was at a place for many years where the CEO was quite bad. He had few skills, both technical and interpersonal. So many people in the organization had strategies for dealing with him, distracting him away from important work. I was always disgusted by the wasted efforts of the entire organization finding ways to route around this CEO, and leaving was one of the best things I ever did.
Within any large company, an internal move is fairly simple stuff and an external move will always be more lucrative in terms of compensation.