Rewrite search URL's to "pretty" permalinks. A custom permalink structure must be set.

rewrite-search-urls.php

<?php
/**
 *
 *	Plugin Name: Rewrite Search URL's
 *	Description: Rewrite search URL's to "pretty" permalinks. A custom permalink structure must be set.
 *	Version:     1.0.1
 *	Author:      James Morrison
 *	Author URI:  https://www.jamesmorrison.me/
 *
 **/

add_action( 'template_redirect', function() {

	// Ensure a permalink structure is set and this is a search results page request
	if ( ! empty( get_option( 'permalink_structure' ) && ! empty( $_GET[ 's' ] ) ) ) {

		wp_redirect( esc_attr( home_url( '/search/' . urlencode( get_query_var( 's' ) ) ) ), 302 );
		exit();

	}

}, 10, 0 );