Do I really have to 301 redirect the “none www.” version of my domain to the “www version” or the other way around? Yes, because if you don’t this can happen:
It happened to one of my clients (ignored my advice). After many years of running that site on the “none www version” Google decided one day that the “www. version” was actually tastier.
You can see the shift of traffic in the screenshot above which I made. So yes, just add that redirect, and set your prefered domain in the Google Search Console.