Don't be a hero in the organization. In the past job. I essentially took over my manager by consistently outshining them. Then they made some unforced errors and I took advantage of the moment, made a political move, and forced their displacement. It was a distinctly unpleasant experience and something I took no glee from doing. Moreover, if you look at the grand scheme of things, nobody remembers that, and you're neither a hero to yourself nor those around you for it. It was a year or two I could have spent finding a productive, healthy, and more facilitating organization.
Your manager is supposed to be the responsible adult in the room, and competent at their job. If that's not true and they're making your life worse, you have no obligation to suffer that.
If you possibly can, make this clear to your manager's manager. Even if it's only at the exit interview.
The one thing I'd add is, be aware of the politics of the organization.
Is this new manager seen by his bosses to be doing a great job? Or are they still trying to get traction?
I once went from the best manager in my career straight to the worst one due to a reorg. But after a couple months it was starting to become clear upper management didn't think he was so great either. So I waited it out and the new manager lasted less than a year. So I didn't have to give up and leave a team & job I otherwise enjoyed. Had I reacted too quickly I probably would've quit in disgust and later regretted it when the bad manager was removed.
I don't think GP was suggesting quitting in a huff, but it's important enough to reiterate.
It's always always always easier to find a job when you have one.
I get the stress of looking, interviewing and negotiating for a new job is a lot on top of the work from your current job.
But, fair or not, there's a worry about hiring a lemon when someone is not currently employed. It's something one can and should address, but it is easier if one does not have to.
Especially in this job marketing (at least in the USA) when getting hired is difficult for everyone.
This doesn't always happen, but it has happened often enough to me, so you might think about the possibility in advance and what you would do.
For myself, I have NEVER taken the counter-offer and stayed. When I have had a bad manager, I regarded that as a failure of my manager's manager as well. I didn't think the situation would instantly be fixed, miraculously, if they did fire my boss or move me to a new position in the same company. But that is just my experience. It would be good if others who have had a different and successful experience staying would speak up too, so you can get the full picture of possible outcomes.
If they don't offer incentive enough to make staying actually worth it, then do not, no matter what guilt trips are applied.
If you get an opportunity for an exit interview, write out a thing pointing out every way in which the terrible manager is terrible.
Encourage your co-workers to do the same.
I’ve worked as a consultant with small and large organizations for most of my career, and I’ve seen this exact situation play out more times than I can count.
If I could go back, I’d tell my younger self not to stick around under bad leadership or in an unhealthy environment. It’s rarely worth it. Even if you care deeply about the mission, a toxic manager will slowly drain your motivation and confidence. I stayed in a few of those situations too long, thinking I had to tough it out. I didn’t, and neither do you.
The projects I’m most proud of were with teams I genuinely enjoyed working and growing with. That’s not a coincidence.
Start quietly looking. The right environment can bring out the best in you in ways this one won’t.
I really hope it works out for you.