A boring as it sounds, your friends and colleagues are right, the conventional advice of not quitting without an offer is correct.

That is the advice can result in unemployment benefits, severance, being a more appealing candidate, and not ending up with a resume gap / weird transition to explain for the rest of your career, as well as obvious benefits like additional/ongoing income.

I suggest doing your best to tackle and overcome issues with being burned out and mental energy while you are still employed. Some of these issues will be down to your job, but a lot of it is also down to you, how you deal with things, setting boundaries, etc, so its a good opportunity to learn skills that will be useful in future workplaces too. I can assure you, this is not the only "very toxic environment" you will encounter.