[Support request] A button with selection function

That URL is for a static page which is display a fixed parameter query loop.
Are you manually creating each of those category pages?

If so would a shortcode with a category argument, where you set the terms to list, work ?

Try this PHP Snippet:

function display_post_links_select_box( $atts ) {
    $output = '';
    
    // Set up the shortcode attributes
    $atts = shortcode_atts( array(
        'category_slug' => '',
    ), $atts );

    // Get the current category ID, or the ID of the specified category slug
    if ( $atts['category_slug'] ) {
        $category = get_category_by_slug( $atts['category_slug'] );
        $category_id = $category->term_id;
    } else {
        $category = get_queried_object();
        $category_id = $category->term_id;
    }

    // Set up the query arguments to get posts in the current or specified category
    $args = array(
        'posts_per_page' => -1,
        'post_type' => 'post',
        'post_status' => 'publish',
        'orderby' => 'title',
        'order' => 'ASC',
        'category__in' => array( $category_id ),
    );

    $query = new WP_Query( $args );
    if ( $query->have_posts() ) {
        $output .= '<select name="post_links" onchange="location = this.value;">';
        while ( $query->have_posts() ) {
            $query->the_post();
            $output .= '<option value="' . get_permalink() . '">' . get_the_title() . '</option>';
        }
        $output .= '</select>';
        wp_reset_postdata();
    }
    return $output;
}
add_shortcode( 'category_posts', 'display_post_links_select_box' );

Then on your page add the shortcode: [category_posts category_slug="your-category-slug"]

Please do 🙂

Are the posts a normal Post ? Or are they custom posts ?