Apply multiple Content Type filters to Search Block Form in hook_form_alter()
So, I figured out how to make it work without actually finding any documentation. I just added a new filter for each content type I want to search:

$form['advanced-form'] = [
    '#type' =&gt; 'hidden',
    '#value' =&gt; 1,
];
// add filter for current language
$form['f[0]'] = [
    '#type' =&gt; 'hidden',
    '#value' =&gt; 'language:' . \Drupal::languageManager()-&gt;getCurrentLanguage()-&gt;getId(),
];
// add filter for each full-page content type
foreach (fullPageNodeList() as $key =&gt; $full_page_type) {
    $form['f['.($key + 1).']'] = [
        '#type' =&gt; 'hidden',
        '#value' =&gt; 'type:'.$full_page_type
    ];
}