My job pays well, but the management is extremely unreasonable. Should I start looking for a new job?

You can start looking for jobs

but at the same time see how you can resolve the issues at work

it can be talking to the managemnt about it

or talk to your boss and ask him what does he want to achieve with his way of doing it this way

I have met quite a few in my career before. Replying emails after work hours seem to be a norm most of my career, but there also comes a point when you know that it's time to consider looking when your team members have the exact same sentiments, and have left because of that.

No harm looking for new opportunities. Update your linkedin, send out some resume, etc. You can always decide again when an offer comes. You'll never know that u will get.

I think being happy or at least not annoyed at work is important for your mental health. If you boss is the cause of your unhappiness then I believe the next best way is to move on. There will be better companies and bosses out there