Group search results by Category in Wordpress

Question

to group search results by Category. Each category should have it ranking:

Search result page:

1. Persons: (results from category "Persons", by relevance) 1 2 3 pagination

2. Companies (results from category "Companies", by relevance)

6. News (results from category "News", by date (newest first)

Here is my code so far:

<?php
get_header();

// Get search visibility option from admin settings
$gecko_settings = GeckoConfigSettings::get_instance();

// Options page settings
$full_width_layout = $gecko_settings->get_option('opt_search_full_width_layout', 0);
// $builder_friendly_layout = get_post_meta(get_proper_ID(), 'gecko-page-builder-friendly', true);

$main_class = 'both';

if ($gecko_settings->get_option('opt_sidebar_left_search_vis', 1) == 1) {
    $main_class = 'main--left';
}

if ($gecko_settings->get_option('opt_sidebar_right_search_vis', 1) == 1) {
    $main_class = 'main--right';
}


if ($gecko_settings->get_option('opt_sidebar_left_search_vis', 1) == 1 && $gecko_settings->get_option('opt_sidebar_right_search_vis', 1) == 1) {
    $main_class = 'main--both';
}


$content_id = "";


if ($gecko_settings->get_option('opt_search_grid', 0) == 1) {
    $content_id = "gecko-blog";
}
?>

<div id="main" class="main <?php echo $main_class;
if ($full_width_layout === 1):
    echo " main--full"; endif; ?>">
    <!-- ABOVE CONTENT WIDGETS -->
    <?php get_template_part('template-parts/widgets/above-content'); ?>
    <!-- end: ABOVE CONTENT WIDGETS -->
    <div <?php if ($content_id): ?>id="<?php echo $content_id; ?>" <?php endif; ?> class="content">
        <?php
        if (function_exists('yoast_breadcrumb')) {
            if ($gecko_settings->get_option('opt_yoastseo_breadcrumbs', 1) == 1) {
                yoast_breadcrumb('<div id="breadcrumbs" class="gc-breadcrumbs">', '</div>');
            }
        }
        ?>
        
        <?php
        // Group search results by category
        $search_categories = array(
            'Persons' => array(),
            'Companies' => array(),
            'News' => array(),
        );

        if (have_posts()):
            while (have_posts()):
                the_post();
                $category = get_the_category();
                if (count($category) > 0) {
                    $category_name = $category[0]->cat_name;
                    if (array_key_exists($category_name, $search_categories)) {
                        $search_categories[$category_name][] = $post;
                    }
                }
            endwhile;
        endif;
        ?>
        
        <?php if (count($search_categories['Persons']) > 0): ?>
            <h2>Persons:</h2>
            <ol>
                <?php 
                // Sort Persons results by relevance
                uasort($search_categories['Persons'], function ($a, $b) {
                    $relevance_a = get_post_meta($a->ID, 'relevance', true);
                    $relevance_b = get_post_meta($b->ID, 'relevance', true);
                    if ($relevance_a == $relevance_b) {
                        return 0;
                    }
                    return ($relevance_a > $relevance_b) ? -1 : 1;
                });
                foreach ($search_categories['Persons'] as $post): ?>
                    <li>
                        <?php the_title(); ?>
                    </li>
                <?php endforeach; ?>
            </ol>
            <?php the_posts_pagination(); ?>
        <?php endif; ?>


        <?php if (count($search_categories['Companies']) > 0): ?>
            <h2>Companies:</h2>
            <ol>
                <?php 
                // Sort Companies results by relevance
                uasort($search_categories['Companies'], function ($a, $b) {
                    $relevance_a = get_post_meta($a->ID, 'relevance', true);
                    $relevance_b = get_post_meta($b->ID, 'relevance', true);
                    if ($relevance_a == $relevance_b) {
                        return 0;
                    }
                    return ($relevance_a > $relevance_b) ? -1 : 1;
                });
                foreach ($search_categories['Companies'] as $post): ?>
                    <li>
                        <?php the_title(); ?>
                    </li>
                <?php endforeach; ?>
            </ol>
            <?php the_posts_pagination(); ?>
        <?php endif; ?>


        <?php if (count($search_categories['News']) > 0): ?>
            <?php
            // Sort News results by date (newest first)
            usort($search_categories['News'], function ($a, $b) {
                $time_a = strtotime($a->post_date);
                $time_b = strtotime($b->post_date);
                if ($time_a == $time_b) {
                    return 0;
                }
                return ($time_a > $time_b) ? -1 : 1;
            });
            ?>
            <h2>News:</h2>
            <ol>
                <?php foreach ($search_categories['News'] as $post): ?>
                    <li>
                        <?php the_title(); ?>
                    </li>
                <?php endforeach; ?>
            </ol>
            <?php the_posts_pagination(); ?>
        <?php endif; ?>


        <?php
        // If no content, include the "No posts found" template.
        if (!have_posts()):
            get_template_part('template-parts/content', 'none');
        endif;
        ?>
    </div>
    <!-- UNDER CONTENT WIDGETS -->
    <?php get_template_part('template-parts/widgets/under-content'); ?>
    <!-- end: UNDER CONTENT WIDGETS -->

Here is what I trying to get:

1. To make the search results clickable
2. To make search results correct. It's return now something not related to request.