How can I set the selected value from a list to an input in vue 3?

I have list that is returned from a request, I have a text input where I search and the list show the results of that search, I want to choose an option from that list I show the selected value in the put where i did the search.
I Tried this but it doesn't show the selected value:

<input type="text" name="project" v-model="project" />
      <div :class="['result',{hidden:!results?.length}]" >
        <ul>
          <li v-for="(result) in results" @click="selectProject(result)">
             {{ result.name}}
          </li>
        </ul>
      </div>



let project = ref('');
let template = ref('');
let results = ref([])
let selectedProject = ref(null);

this is where I tried to set the selected value when i click one of the options from the result list

const selectProject = (project) => {
  project.value = project.name
  selectedProject.value = project.id
  results.value = []
  
}

Mr. R is right. Here is the fix.

const selectProject = (value) => {
    project.value = value.name;
    selectedProject.value = value.id;
    results.value = [];
} 

Playground

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

const { createApp, ref } = Vue;

const App = {
  setup() {    
    const project = ref('');
    const template = ref('');
    const results = ref([
      { id: 1, name: 'Projekt 1' },
      { id: 2, name: 'Projekt 2' },
      { id: 3, name: 'Projekt 3' }
    ]);
    const selectedProject = ref();    
    const selectProject = (value) => {
      project.value = value.name;
      selectedProject.value = value.id;
      results.value = [];
    } 
    return { 
      project,
      template,
      results, 
      selectedProject,
      selectProject
     }
  }  
}

const app = createApp(App);
app.mount('#app');

<!-- language: lang-css -->

#app { line-height: 1.5; }
[v-cloak] { display: none; }
li { cursor: pointer; text-decoration: underline; color: blue;}

<!-- language: lang-html -->

<div id="app" v-cloak>  
  Select project: {{selectedProject}} <br/>
  <input type="text" name="project" v-model="project" />
  <div :class="['result',{hidden:!results?.length}]" >
    <ul>
      <li v-for="result in results" @click="selectProject(result)">
         {{result.name}}
      </li>
    </ul>
  </div>
</div>
<script src="https://unpkg.com/vue@3/dist/vue.global.prod.js"></script>

<!-- end snippet -->