I'm responding because I also quit a job years ago to preserve my mental health, so your post resonates with me. When I quit, I was becoming increasingly depressed. I did not have a new job lined up. I did have several years of $$ runway. I also considered it an option to move to a cheaper COL area overseas, if needed, to keep afloat.
Since then, I've mostly taken gig work to provide for myself (freelance/consulting software development - mostly mobile app development, but also web app stuff).
I don't know how typical your experience was for "state work". If I were you, I might try to leverage my previous experience into a new state job, which might turn out better.
My answers to your bullet points aren't really relevant, since I left my last FT job over 10 years ago. But I'll give them anyway.
Locating: In one case, I got a referral from a friend who had interviewed with the company and didn't like the place (he was right, I was more desperate and took the offer). In all other cases, I found the job via a recruiter. However, I don't recommend using a recruiter, and I think you're better off using your network, if you have one. Using recruiters was unpleasant for me, to say the least. I'm not saying all recruiters are bad, just that the ones I interacted with were far from awesome. At least they got my foot in the door before pumping me for the interview questions on the way out the door.
Interviewing: I read a couple of books on interviewing, did a very small amount of l33t code style practice (which I found boring and didn't seem helpful). I looked for sample interview questions and practiced writing down responses. I think live in-person mock interviews would have been helpful, but I didn't have anyone to practice with. I looked back on my old jobs and tried to imagine creative ways of making it sound like I'd been a positive contributor (which I was, but sometimes you feel powerless to make much of an impact at the time, so everything you did seemed pointless looking back at it).
Surviving: My "job lifetime" - defined as how long I can stand a job without feeling like I'm going out of my mind - seemed to be about 1.5 to 3 years (the first 6 months is the honeymoon phase where I'm learning a lot, and then gradually I start to know what's what, and I get disillusioned). It seemed to decrease after each job, which is probably why I decided to go with gig work after my last position. I wish I could tell you about surviving, but I didn't "survive" my jobs very well. You might want to try gamifying things, something that never occurred to me at the time. Since you're planning to quit anyway, pretend that whatever you do doesn't much matter, and just do your job however you want (within reason - nothing illegal!) so that at least you are getting something out of it. Maybe this wouldn't have been possible with your old job. In my jobs, I definitely saw coworkers get away with things that I thought were "wrong," but were clearly tolerated by management, so I think I had more leeway than I realized at the time.
Take work less seriously? It's there to pay the bills. It's a waste of your time on earth, but you also probably don't want to be on the street, which would also be a waste of your time, and much more unpleasant. You might try gig work, if you can find it, and see if that agrees with you. Usually the gigs are a little more transactional, and sometimes you find ones that are actually fun with cool people. Churn is expected - no one finds it strange that you left a gig after 3 months.
You can take the opposite tack and try creating your own work out of what you love, a la Will Shortz https://en.wikipedia.org/wiki/Will_Shortz My feeling is that this is just not possible unless you're pretty narrowly passionate about one thing. And not everyone wants to make their passion into a profession.