If the current job is causing a lot of stress/burnout, carrying that into a new role is setting yourself up for failure. Having a few months gap isn't a problem IME and it helps with recovery.
You will be exponentially more attractive to recruiters while employed. Recruiters/HR will treat you as high value and will value your time a lot more if you are just changing jobs.
The opposite is true for someone looking for opportunities whilst unemployed, irrespective of industry experience.
The difference in recruited experience is massive having experienced both scenarios. It is just an unavoidable human bias from future employers.