Not disagreeing with you, but OP specifically mentions being burned out, and I think for this specific situation it may be better to cut losses and go elsewhere.

If you have the energy and enthusiasm for fixing broken things, this is great advice, ideally before the point of burnout / before six months (but after at least a month or so). But not every senior role has to involve cleaning up messes and picking political fights. You're allowed to look for a company that isn't a mess if you want.