[Vuejs]-Why does Vuetify Autocomplete not selecting the data being set?

It looks like you overriding job twice: on the onChangeJob method and via v-model on JobDropdownSelector.

You can try use input event to update modek instead of emitting additional event.

JobDropdownSelector.vue

methods: {
  onChange(e) {
    // You don't need set job because it's connected via v-model.
    // this.job = e; 
    this.$emit("input", e);
  }
}

This will cause that job in EditForm.vue should update automatically after dropdown change.