My view may not be what you want to hear but you should stay but be actively looking for a job.

A few years back in my first job I knew I didn’t like it the second week in. Eventually I got a job and left after eight months.

It is 1) always more presentable when you at least have a job vs being jobless to hr and 2) when you have a convincing story for why you are looking, nobody really bats an eye and 3) potential of lost income