I've been using magnetic cables for almost a decade. I use them with all of my iPhones, Android phones, headsets, battery packs, etc. Pretty much all small devices with a micro USB, USB-C, or lightning port.
They worked fine for years with my iPhone 5, iPhone SE, and iPhone SE 2.
With my iPhone 13 Pro, the first time I plug it in, it works and I'm able to charge. But the next time I go to charge, sometimes it won't work and I'll have to either reboot the phone or take the tip out and put it back in — and then it works.
I've tried numerous tips and the same tip on other phones. There is nothing wrong with the cables or tips.
Could the phone be doing something to prevent it from working? It works again if I reboot, so I don't think it is a physical issue.