Here's my full Options API version with debounce, preserveState and replace in case it might be of help to anyone:

<script>
import {Link} from '@inertiajs/inertia-vue3';
import Pagination from '../../Shared/Pagination';
import {debounce} from "lodash";


export default {
    name: "Users",
    components: {Link, Pagination},
    props: {
        users: Object,
        filters: Object
    },
    data() {
        return {
            search: this.filters.search
        }
    },
    watch: {
        search: debounce(function (value) {
            this.$inertia.get('/users', {search: value}, {
                preserveState: true,
                replace: true
            })
        }, 300)
    }
}
</script>

Better Performance With Throttle and Debounce