Depends a lot on what you have to stand on. Got FANG on your resume? or NASA or something? Coast through your career if you want. Fresh out of a bootcamp or a college that isn't One Of Those Big Ones? Yea, a project is a great way to prove you know your stuff.
Having a project I was actively working during my job search was great for a lot of other reasons, too. A lot of interviewers don't really know what to talk about, hadn't looked at my resume, etc. I could quickly take control of these interviews by bringing up my project, and many interviewers would seem almost relieved to have the pressure taken off of them. This had relatively obvious advantages for me insomuch as I controlled the narrative of the interview, came off as very competent (despite having literally no working experience), and left interviewers with a good impression. All in all I consider this, along with my volume of applications, to be the most important aspect of my job search.
Having a project I was actively working during my job search was great for a lot of other reasons, too. A lot of interviewers don't really know what to talk about, hadn't looked at my resume, etc. I could quickly take control of these interviews by bringing up my project, and many interviewers would seem almost relieved to have the pressure taken off of them. This had relatively obvious advantages for me insomuch as I controlled the narrative of the interview, came off as very competent (despite having literally no working experience), and left interviewers with a good impression. All in all I consider this, along with my volume of applications, to be the most important aspect of my job search.