Simple search form with results page

To add a Select dropdown field to your text search you can modify the form like this:

add query vars
sanitize the query string
make the form
set the query arguments from the string
run the wp_query

1. add query vars (functions.php)

<?php
 function custom_search_query_vars_filter($vars) {
	$vars[] .= 'cs_text_field';
    $vars[] .= 'cs_category_name';
	return $vars;
}
add_filter( 'query_vars', 'custom_search_query_vars_filter' );
?>

2. sanitize the query string (parts/search/searchform-categories.php)

<?php
$textField = sanitize_text_field(get_query_var('cs_text_field'));
$filterByCategory = sanitize_text_field(get_query_var('cs_category_name'));

3. the form (parts/search/searchform-categories.php)

<form role="search" method="get" action="<?php $_PHP_SELF ?>#searchform" id="searchform" class="wp-block-search__button-outside wp-block-search__text-button wp-block-search">
	<label for="wp-block-search__input-1" class="wp-block-search__label">Search the site</label>
	<div class="wp-block-search__inside-wrapper ">
		<input type="search" id="wp-block-search__input-1" class="wp-block-search__input " name="cs_text_field" value="<?php echo $textField ?>" placeholder="Text Search..." >
	</div>
	<hr class="clearfix" />
	<label for="wp-block-search__input-2" class="wp-block-search__label">Category</label>
	<div class="wp-block-search__inside-wrapper ">
		<select name="cs_category_name">
			<option value="" >Select below:</option>
			<?php 
				$args = array(
					'exclude' => '1'
				);
				
				$categories = get_categories( $args );
				foreach ( $categories as $category ) {
				$selected = $category->slug === $filterByCategory ? 'selected' : '';
														
				echo '<option value="' . $category->slug . '" ' . $selected . '>' . $category->name . '</option>';
				} 
				?>
			</select>
	</div>
	<hr class="clearfix" />
	 <button type="submit" class="wp-block-search__button  ">Search this site</button>			
</form>

<form role="search" method="get" action="<?php $_PHP_SELF ?>#searchform" id="searchform" class="wp-block-search__button-outside wp-block-search__text-button wp-block-search">
	<label for="wp-block-search__input-1" class="wp-block-search__label">Search the site</label>
	<div class="wp-block-search__inside-wrapper ">
		<input type="search" id="wp-block-search__input-1" class="wp-block-search__input " name="cs_text_field" value="<?php echo $textField ?>" placeholder="Text Search..." >
	</div>
	<hr class="clearfix" />
	<label for="wp-block-search__input-2" class="wp-block-search__label">Category</label>
	<div class="wp-block-search__inside-wrapper ">
		<select name="cs_category_name">
			<option value="" >Select below:</option>
			<?php 
				$args = array(
					'exclude' => '1'
				);
				
				$categories = get_categories( $args );
				foreach ( $categories as $category ) {
				$selected = $category->slug === $filterByCategory ? 'selected' : '';
														
				echo '<option value="' . $category->slug . '" ' . $selected . '>' . $category->name . '</option>';
				} 
				?>
			</select>
	</div>
	<hr class="clearfix" />
	 <button type="submit" class="wp-block-search__button  ">Search this site</button>			
</form>

4. set the query arguments from the string (parts/search/searchform-categories.php)

<?php 
$args = array(
	'post_type' => 'post', 
	'posts_per_page' => -1, 
	'post_status' => 'publish',
	'ignore_sticky_posts' => true
);

if (!empty ($textField) ) {
	$newArgs = array(
		's' => $textField,
	);
	$args = array_merge($args, $newArgs);
}
if (!empty ($filterByCategory) ) {
	$newArgs = array(
		'category_name'		=> $filterByCategory,
	);
	$args = array_merge($args, $newArgs);
}

5. the wp_query (parts/search/searchform-categories.php)

<?php 
$q = new WP_Query( $args );
?>
<?php if($q->have_posts()): ?>
    <?php while($q->have_posts()): $q->the_post() ?>
        <a href="<?php the_permalink(); ?>"><?php the_title(); ?>
		<?php 
            $categories = get_the_category();
			if ( ! empty( $categories ) ) {
				echo ' - ';
				echo esc_html( $categories[0]->name );	
			}
             ?></a><hr />
    <?php endwhile; ?>
<?php endif; ?>