Definitely start interviewing, but in order to do so you will have to stop working unpaid overtime for your company. Since you're already leaving anyway, promotions or looking to get ahead of your peers is out the window, so focus on yourself, and not your work. That's the most important step! Keep it 9-5.
Increasing, the hiring landscape is becoming more hostile to us. I guess you got lucky (congrats), but I would not count on that. Companies are always out looking for cheap employees, and the power dynamic is almost entirely in the favor of companies. So I would really encourage (for OP) to make careful plans, backup plans, rather than rely on luck itself.
Also OP, we get you're exhausted from overworking. It's also ok to take vacation before you start your interview journey. Recharge a little, it'll make a huge difference when you're going into an interview headstrong rather than tired out.
At higher paying ones, you might have to do a HR filtering interview, code test, hour long chat with an engineer, a higher level manager, a whiteboard, another code test, and then present it to a panel which consists of four engineers... and possibly get rejected somewhere along this route. Some of the people in this process are not always there and they may not put hiring at first priority, so this can drag out very long.
If you have a "runway", you'll be under pressure to perform, which ironically might make you screw up somewhere along the process as I have before. It's so much easier just to settle for the lower paying job.
And as someone who has been on the hiring side, I've seen people who we wanted to hire, but failed because of this pressure. Two people who were going through extended interviews just refused to do an hour long coding challenge properly (they lazily copied something from SO which didn't answer the question). One interviewee snapped at the interviewer during the test. The process was also quite long because we didn't really need another person, so it took about 2-3 months to get back to the second guy we interviewed, who wasn't that qualified but better than the others.
However, if you're facing intense stress and burnout, the lower paying job might be a step forward.
Just be somewhat proficient and you'll be fine!
My last few jobs were all left with no other job in place and i think the longest it took to find a new position was three weeks.
I've also done this and had another job in three years.
Once you get get a job offer tell them you can't start for a month. If that's ok with them, accept and put in your 2 weeks, and get 2 weeks unpaid in-between jobs to unwind before starting your new journey.
The last time I switched jobs, I even negotiated a 3-4 weeks paid leave as I had PTO I wanted to take from my previous job, but they wanted me to start earlier than 1.5 months (the date I gave them mentioning I wanted to take my vacation at my old job). They hired me and let me take 3 weeks off after working for 2 weeks and it was all on payroll not affecting my annual PTO hours.
I'm taking two days off at the moment. I woke up with the reality no one will contact me with an IT issue. My new life has it's pressures however I enjoy the less frantic environment.
Talking from personal experience, as I am a "good worker", and tend to take up every problem I see and solve it. Which is kind of self-exploiting and not sustainable in the long-run. I have to actively remind myself that setting limits and communicating them is part of the job, as otherwise you'll end up burnt out. The difficulty here is, it may be even okay in some short-time frame, it is not black and white.
Just food for thought: Would it be an option to be also frank about it to future employers? E.g. I am currently not at the top of my skills due the current work-load. Would they be willing to re-negotiate after a certain time of working part-time to recover?
Personally, I value in a company (or team) more that they treat you humanely, than having a pay-check which is possibly three times as high as now. But that is the luxury of having a high salary.
If it is at all possible for you to take a leave of absence or reduce you workload, that would probably be a better option. You might feel burnt out now, but being unemployed adds its own type of stress.
As part of your joining procedure, the new company's HR will necessarily ask for past 3 months payslips from the previous employer. And if the numbers don't match what was disclosed, they quickly rescind the offer.
And definitely don't quit without finding the next job. You will be under a lot more stress and it would affect your performance.
In 8 months you can certainly find another job, but more likely you’ll want to spend a little time decompressing. Don’t worry too much about it, software developers are still in very good demand.
Outside of that, quitting a job before you have a new one makes it more challenging to get a new job. Recruiters and employers find those that have a job more favourable plus it gives you a negotiating advantage when it comes to salary.
Read my post about contract jobs if you do quit and have trouble finding something new.