How to update the page and query parameters in SvelteKit?

I have a page with a search field. If accessed with a query parameter (e.g. ?word=cat) the page should load with results present and the search field filled. If a search is done the results and the query parameters (browser history) should update.

The only way I found to update query parameters is goto, so my attempt is:

<script context="module">
  export async function load({ page, fetch }) {
    const response = await fetch(`/data.json?${page.query.toString()}`)
    if (response.ok) {
      return {
        props: {
          word: page.query.get('word'),
          body: await response.json()
        }
      }
    }
  }
</script>

<script>
  import { goto } from '$app/navigation'
  import { page } from '$app/stores'

  export let word
  export let body

  function search() {
    $page.query.set('word', word)
    goto(`?${$page.query.toString()}`)
  }
</script>

<main>
  <form on:submit|preventDefault={search}>
    <input bind:value={word}>
  </form>
  <!-- ... -->
</main>

This works but sometimes gets stuck just updating the query parameters and nothing else. For some reason load isn't being called in those cases. I can get it to work reliably by adding await invalidate for the URL before the goto, but now load is always called twice and the search field flips back to the old value shortly.

I just started with Svelte/SvelteKit, so my approach is probably just wrong. Thanks for any help.

I had similar issue triggering load function and I solved it by creating new instance of the URLSearchParams and navigating to these new params.

let query = new URLSearchParams($page.url.searchParams.toString());
    
query.set('word', word);
        
goto(`?${query.toString()}`);