feat(place-search-bar-below-navbar): add search bar model to the navbar search bar wrapper component

src/features/nav/components/NavbarSearchBarWrapper.vue

@@ -17,14 +17,27 @@ limitations under the License.
 <script setup>
 import Searchbar from '@/features/search/components/Searchbar.vue';
 
+import { watch } from 'vue';
 import { useRoute } from 'vue-router';
 
 const route = useRoute();
+const searchQueryModel = defineModel();
+
+watch(() => route.name, name => {
+    searchQueryModel.value = name === 'searchResults' ? route.query.q || '' : '';
+});
+
+watch(() => route.query.q, q => {
+    if (route.name === 'searchResults') {
+        searchQueryModel.value = q || '';
+    }
+});
 </script>
 
 <template>
     <Searchbar
         v-if="route.name === 'searchResults'"
+        v-model="searchQueryModel"
         auto-submit
     />
 </template>