How to call method in setup of vuejs3 app?

You could use composition and options api in the same component but for different properties and methods, in your case the data properties could be defined inside setup hook using ref or reactive, the methods could be defined as plain js functions :

import {ref} from 'vue'
export default {
  name: 'adminCategoriesList',
  mixins: [appMixin],
  components: {
  },
  setup () {
    const categoriesPerPage= ref(20);
    const currentPage=ref(1);
    const categoriesTotalCount=ref(0),
    const categories=ref[])

    const adminCategoriesListInit = async () => {
      loadCategories()
    }

    function onSubmit (credentials) {
      alert(JSON.stringify(credentials, null, 2))
    }

    functions loadCategories(){
      ...
    }

    onMounted(adminCategoriesListInit)

    return {
      // schema,
      onSubmit,
      categoriesPerPage,
      currentPage,
      categoriesTotalCount,
      categories
    }
  },

the properties defined by ref could be used/mutated by property.value and used in template like {{property}}