I think there's a nuance in this that's easy to be missed. It's possible to care about the quality of your work but not care about the various forms of insanity in your management chain.
I think a lot of people fear that not caring means you turn into a totally useless person - that extremely unproductive person in the company that everybody hates but management and HR refuses to fire.
Not caring doesn't mean you have to become that person.
> I find I’m more productive than I’ve been in years because I’m not worrying if something takes longer than expected or is bigger than I realised. I can just enjoy the problem solving and shipping without the stress.
100% this. Care about the quality of your work. If you work for a place where that's never possible due to constant unrealistic expectations, start looking for another place to work.
I've actually found that some managers like employees who don't care so much because they need much less care and feeding. People who care too much also complain too much. And even if you do good work, constant complaining can overshadow that.