Going back to a url doesn't update the page

There's a page showing a student list. It should support pagination (via ?page=).

Going from ?page=0 to ?page=1 -> page is updated

Going back from ?page=1 to ?page=0 -> page is not updated (unless I pass invalideAll:true - goto('?page=0', { invalidateAll:true })

// +page.tsimport type { PageLoad } from './$types';export const prerender = true;export const load: PageLoad = async ({ fetch, url }) => {    const selected_page = parseInt(url.searchParams.get("page") || "0");    const res = await fetch(`/api/student-list?page=${selected_page}`); // make sure there are no trailing slashes, otherwise bug https://stackoverflow.com/questions/78734150/sveltekit-redirect-308-when-trying-to-access-internal-api-from-page-server-ts    const response = await res.json();    response.selected_page = selected_page + 1;    console.log("load() selected page=", selected_page);    return response;};

<!-- +page.svelte --><script lang="ts">    import Pagination from "../../components/pagination.svelte";    /** @type {{ data: import('./$types').PageData }} */    import { page as g_page } from "$app/state";    import { goto } from "$app/navigation";    const { data } = $props();    const _ = $derived(data); // to make sure when 'data' is updated, things are re-rendered    const __ = $derived(g_page.url.searchParams);    function page_clicked(page_arg: number) {        g_page.url.searchParams.set("page", (page_arg - 1).toString());        goto(g_page.url);    }</script><Pagination custom_class="mb-8"    onPageClick={page_clicked}    selected_page={data.selected_page}    total={data.total}/>

Is there a way to fix this? is this by-design?