Output SearchWP Live Ajax Search results grouped by Category taxonomy term

search-results.php

<?php
/**
 * Search results are contained within a div.searchwp-live-search-results
 * which you can style accordingly as you would any other element on your site
 *
 * Some base styles are output in wp_footer that do nothing but position the
 * results container and apply a default transition, you can disable that by
 * adding the following to your theme's functions.php:
 *
 * add_filter( 'searchwp_live_search_base_styles', '__return_false' );
 *
 * There is a separate stylesheet that is also enqueued that applies the default
 * results theme (the visual styles) but you can disable that too by adding
 * the following to your theme's functions.php:
 *
 * wp_dequeue_style( 'searchwp-live-search' );
 *
 * You can use ~/searchwp-live-search/assets/styles/style.css as a guide to customize
 */

if ( ! have_posts() ) : ?>
	<p>No results</p>
<?php return; endif; ?>

<?php

global $post;
$grouped_results = [];
$no_term_results = [];

while ( have_posts() ) {
	the_post();

	$categories = get_the_terms( $post,'category' );

	// Group by the first Category returned.
	if ( ! empty( $categories ) && isset( $categories[0] ) ) {
		// If this group doesn't exist yet, create it.
		if ( ! array_key_exists( $categories[0]->term_id, $grouped_results ) ) {
			$grouped_results[ $categories[0]->term_id ] = [
				'term'    => $categories[0],
				'results' => [],
			];
		}

		// Add this result to the group.
		$grouped_results[ $categories[0]->term_id ]['results'][ $post->ID ] = get_post( $post->ID );
	} else {
		$no_term_results[ $post->ID ] = get_post( $post->ID );
	}
}

// Output grouped results.
if ( ! empty( $grouped_results ) ) {
	foreach ( $grouped_results as $grouped_result ) {
		echo '<h3>' . esc_html( $grouped_result['term']->name ) . '</h3>';
		foreach ( $grouped_result['results'] as $result ) {
			?>
			<div class="searchwp-live-search-result" role="option" id="" aria-selected="false">
				<p>
					<a href="<?php echo esc_url( get_permalink( $result->ID ) ); ?>">
						<?php echo wp_kses_post( get_the_title( $result->ID ) ); ?> &raquo;
					</a>
				</p>
			</div>
			<?php
		}
	}
}

// Output ungrouped results.
if ( ! empty( $no_term_results ) ) {
	foreach ( $no_term_results as $result ) {
		?>
		<div class="searchwp-live-search-result" role="option" id="" aria-selected="false">
			<p>
				<a href="<?php echo esc_url( get_permalink( $result->ID ) ); ?>">
					<?php echo wp_kses_post( get_the_title( $result->ID ) ); ?> &raquo;
				</a>
			</p>
		</div>
		<?php
	}
}