How to add meta field to REST API Response of a WordPress Posts using register_rest_field?

WP REST API register_rest_field().

You can use the register_rest_field() function to add additional meta key to the REST API
eg: 

add_action( 'rest_api_init', 'create_api_posts_meta_field' );
 
function create_api_posts_meta_field() {
 
    // register_rest_field ( 'name-of-post-type', 'name-of-field-to-return', array-of-callbacks-and-schema() )
    register_rest_field( 'post', 'banner_image', array(
           'get_callback'    => 'get_post_meta_for_api',
           'schema'          => null,
        )
    );
}
 
function get_post_meta_for_api( $object ) {
    //get the id of the post object array
    $post_id = $object['id'];

    return get_post_meta( $post_id );
}

By using this code you will get the API response contain the key as "banner_image" and value contain the meta data of the post.