change: value= "text" to vMube model = "text"

I think you use: value just assigns the initial value of the text variable to input, but the change in the value of input does not change the text variable, so the value has not changed.
if you want to unify the two, you still have to use v-model for two-way binding

it will be troublesome to manually modify the this.text, in the keydown method every time without two-way binding.

you directly use : value= "text" is equivalent to one-way binding. Every time vue resets render, it will reset input to the value of text, that is, 'vue',' you have assigned hasWarning in your keydown, which will trigger render, so the value of input will become 'vue'.. This can also be well understood from your first demonstration. You change num, every second to trigger render, so every second the value of input will be reset to vue.

is not a problem with keydown. Value is changed according to text, and you need to change text

in keydown. How can you tell that the hasWarning attribute has not changed?

to

keydown() {
      if (1 == 1) {
          this.hasWarning = true;
      }else {
          this.hasWarning = false;
      }
      
    }