Vue3.3.2 - Is it possible to access useRoute within a composable function?

I'm trying to access useRoute from within a composable function. Starting with vue 3.3.2 & vue-route 4.2.0, I set up a test using npm init vue@latest with the router enabled. No problem accessing useRoute via the composition API within the 'script setup' tag:

App.vue

<script setup>
import { RouterLink, RouterView } from 'vue-router'

import { useRoute } from 'vue-router'
const route = useRoute()

import { computed } from 'vue'
const path = computed(() => {
  console.log(`step 1`)
  if (!route) {
    console.log(`step 2`)
    return
  }
  if (!route.path) {
    console.log(`step 3`)
    return
  }
  console.log(`step 4`)
  return route.path
})
</script>

<template>
  <p>path = {{ path }}</p>
  <header>
    <nav>
      <RouterLink to="/">Home</RouterLink>
      <RouterLink to="/about">About</RouterLink>
    </nav>
  </header>

  <RouterView />
</template>

In the above code, the computed function is re-calculated each times the route changes, reaching step 1 then step 4 (success).

But when I move this code to a composable it breaks:

App.vue

<script setup>
import { RouterLink, RouterView } from 'vue-router'
import path from '@/composables/useRouteTest'
</script>

composables/useRouteTest.js

import { useRoute } from 'vue-router'
const route = useRoute()

import { computed } from 'vue'
const path = computed(() => {
  console.log(`step 1`)
  if (!route) {
    console.log(`step 2`)
    return
  }
  if (!route.path) {
    console.log(`step 3`)
    return
  }
  console.log(`step 4`)
  return route.path
})

export default {
  path
}

Within the composable, the computed function never progresses beyond step 2, and is only called once, even when I navigate to different routes.

Does useRoute not work within composables?

I've spend many hours trying the following alternatives: different Vue versions; using watch instead of computed; 'useRouter' rather than 'useRoute'; using watch with async invocation (https://router.vuejs.org/guide/advanced/composition-api.html). Always the same result.

useRoute is only available for use inside script setup. What you can do in the composable is wrap its usage in a function then import and call the function from your component. This is the recommended way to make most composables so they can share the context of the component they're called from.

composables/useRouteTest.js

import { useRoute } from 'vue-router'
import { computed } from 'vue'

export function useRouteTest() {
  const route = useRoute()

  const path = computed(() => {
    console.log(`step 1`)
    if (!route) {
      console.log(`step 2`)
      return
    }
    if (!route.path) {
      console.log(`step 3`)
      return
    }
    return route.path
  })

  return {
    path
  }
}

App.vue

<script setup>
import { useRouteTest } from '@/composables/useRouteTest'

const { path } = useRouteTest()
</script>