If you open login form and link on different devices, you'll get code to type, no need to send link.
So basically you start login on phone, keep page open. Open laptop, click on link on laptop and you'll get a code. You type that code on your phone and that's all.
Even if that's correct, I should not need to use a second device to log in because of some asinine decision not to have a password field.
Solving problems that don't exist, and creating problems that don't need to.