I think the quit first and find a new gig later thing is a bit of a personal preference. some people do better with that cold turkey, walk out the door style. In my experience I’ve always been better about finding a job when I have a job. But I like to be truthful. I have told past bosses that a situation is not sustainable for me and it will lead to me leaving if there isn’t change. With this fair shot across the bow I then spool down a bit, enforcing more strict boundaries on my time and emotional commitment to the job so I can use that extra time and energy to get after finding a new position. Then when I leave I reference the previous conversation, “remember 6 months ago when I said this particular thing would lead to me leaving? That time has come unfortunately…” or something like that.
However you do it, make sure it is authentic to you.