chore(InputMenu): handle async search with search prop

docs/components/content/examples/InputMenuExampleSearchAsync.vue

@@ -0,0 +1,26 @@
+<script setup>
+const loading = ref(false)
+const selected = ref()
+
+async function search (q) {
+  loading.value = true
+
+  const users = await $fetch('https://jsonplaceholder.typicode.com/users', { params: { q } })
+
+  loading.value = false
+
+  return users
+}
+</script>
+
+<template>
+  <UInputMenu
+    v-model="selected"
+    :search="search"
+    :loading="loading"
+    placeholder="Search for a user..."
+    option-attribute="name"
+    trailing
+    by="id"
+  />
+</template>

docs/content/3.forms/2.input-menu.md

@@ -126,6 +126,20 @@ componentProps:
 ---
 ::
 
+### Async search
+
+Pass a function to the `search` prop to customize the search behavior and filter options according to your needs. The function will receive the query as its first argument and should return an array.
+
+Use the `debounce` prop to adjust the delay of the function.
+
+::component-example
+---
+component: 'input-menu-example-search-async'
+componentProps:
+  class: 'w-full lg:w-48'
+---
+::
+
 ## Popper
 
 Use the `popper` prop to customize the popper instance.