functions.php

<?php

// Adds a SearchWP Engines dropdown to the search form
// @link https://searchwp.com/documentation/knowledge-base/engine-select-dropdown/
function my_searchwp_get_search_form_with_engines_dropdown( $form ) {
	ob_start(); ?>
		<form role="search" method="get" class="search-form" action="<?php echo esc_url( home_url( '/' ) ); ?>">
			<label>
				<span class="screen-reader-text">Search For</span>
				<input type="search" class="search-field" placeholder="Search..." value="<?php echo esc_attr( get_search_query() ); ?>" name="s" title="Search for:" />
			</label>
			<?php
				$engines = \SearchWP\Settings::get_engines();
				$current_engine = isset( $_GET['swpengine'] ) ? esc_attr( $_GET['swpengine'] ) : 'default';
			?>
			<select name="swpengine" id="swpengine">
			<?php foreach ( $engines as $engine_name => $engine ) : ?>
				<option value="<?php echo esc_attr( $engine_name ); ?>"
					<?php selected( $current_engine, $engine_name ); ?>>
					<?php echo esc_html( $engine->get_label() ); ?>
				</option>
			<?php endforeach; ?>
			</select>
			<input type="submit" class="search-submit" value="Search" />
		</form>
	<?php return ob_get_clean();
}

add_filter( 'get_search_form', 'my_searchwp_get_search_form_with_engines_dropdown' );