The trick is to un-learn that helplessness by retraining yourself with small steps in the right direction. Jumping straight into hours of Leetcode grinding isn't a good small step. Setting a goal to solve 2 Leetcode problems per week is a good first step. Or even better, maybe skip the Leetcode and start pinging your network for any job openings. Not every job requires Leetcode practice.
> Vacation doesn't help. It just puts me farther behind.
Time to force some control over your workload. Does your manager try to shame you into not taking vacation? Or do they expect you to accomplish the same work whether your on vacation or not? Time to push back.
If you're burned out and thinking of quitting anyway, what's the worst that can happen? As it turns out, you're not actually going to get fired quickly at most any company for simply limiting your workload to something reasonable. There's a hiring crunch right now and they'd have to replace you with someone else. Then you'd just get another job, which is what you wanted anyway. Time to start setting some boundaries, leading with expectations instead of waiting for them to be applied to you, and forcing some vacation time into your schedule. No one is going to make vacation happen for you, so get it done.
Meanwhile, it's time to find another company. I agree that quitting isn't a great idea if it can be avoided. I've seen enough people quit due to burnout and/or depression, only to spiral further into burnout/depression in the ensuing loneliness and financial stresses. Better to switch to a new job where people actually enjoy working together.