How to use v-model and value in one input?

Question

Vue.js

There is

<input type="search" placeholder="Поиск" class="search__input" v-model="search" @keyup.enter="onSearchLineChanged(search)">

which sends the search value to the state (Vuex) on the onSearchLineChanged(search) event. In another component, on click, this search is replaced in state with a different value.
So I need that when this value is replaced (by clicking in the second component), it becomes value. for this input

Answer 1

In the components, watch the value from vuex, something like this (yes, instead of different components, there are several instances of one, but I think the point is clear):

watch: {
  '$store.state.search'(val) {
    this.search = val;
  },
},

Answer 2

Well, put a getter from the state as a model.