You need to wait for sync call :

const app = Vue.createApp({
  data() {
    return {
      product: 1,
      stores: [],
      errors: [],
    };
  },
  methods: {
    async fetchProduct(productId) {
      await axios.get(`https://api.escuelajs.co/api/v1/categories/${productId}/products`)
        .then((res) => {
          this.stores = res.data;
        })
        .catch((e) => {
          this.errors.push(e);
          console.error(e);
        });
    },
    handleClick(productId) {
      this.product = productId;
      this.fetchProduct(productId);
    },
  },
  async created() {
    await this.fetchProduct(this.product);
  },
})
app.mount('#demo')

<script src="https://unpkg.com/vue@3/dist/vue.global.prod.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/axios/1.2.2/axios.min.js" integrity="sha512-QTnb9BQkG4fBYIt9JGvYmxPpd6TBeKp6lsUrtiVQsrJ9sb33Bn9s0wMQO9qVBFbPX3xHRAsBHvXlcsrnJjExjg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script>
<div id="demo">
  <button @click="handleClick(3)">get productid 3</button>
  {{stores}}
</div>

The first answer is correct, so I will not duplicate it, but I see room for improvement in your code/example.

Your useGetProducts hook is very easy to break and hard to reuse. If you will pass the wrong URL or the structure of the API will change it will break your code. Also, the hook is not very generic, cause you will need to create similar fn for each entity. My suggestion. Use react-query and separate functions for calling API. So it will look like this.

import { useQuery } from 'react-query'
import axios from 'axios'

export default function ProductPage() {
  const productResponse = useQuery('exchanges', () => getProduct('6'))
  const { isLoading, isError, data: product } = productResponse

  return (
    <div>
      {isLoading && <div>Loading...</div>}
      {isError && <div>Something went wrong :(</div>}

      {product && (
        <div>
          <h1>Product title: {product.title}</h1>

          <p>
            {product.images.map(imageSrc => (
              <img key={imageSrc} src={imageSrc} alt="" />
            ))}
          </p>
        </div>
      )}
    </div>
  )
}

interface Product {
  id: string
  title: string
  images: string[]
}

function getProduct(id: string): Promise<Product> {
  return axios
    .get(`https://api.escuelajs.co/api/v1/products/${id}`)
    .then(r => r.data)
}

PS. react-query requires additional configuration ( context provider, config, etc ). Please look into docs on how to use it.