Validate rest-api call on create

As I said in the comments, since it’s a custom endpoint, you could just cancel the post creation via the main callback, i.e. something like so:

'callback' => function () {
    if ( some condition ) {
        // create the post
    } else {
        // return existing post or something else
    }
}

And here’s an example where the POST endpoint creates a published post (of the post type), but only if there’s no existing published post having the same title as specified in a parameter named title:

Note: When registering custom REST routes, use your own namespace (e.g. my-namespace/v1) and not wp/v2.

add_action( 'rest_api_init', function() {
    register_rest_route( 'my-namespace/v1', '/foobar', array(
        'methods'             => 'POST',
        'callback'            => function ( $request ) {
            $posts = get_posts( array(
                'post_type' => 'post',
                'title'     => $request['title'],
                'fields'    => 'ids',
            ) );

            if ( ! empty( $posts ) ) {
                return new WP_Error(
                    'rest_post_exists',
                    'There is already a post with the same title.',
                    array( 'status' => 400 )
                );
            }

            return wp_insert_post( array(
                'post_type'   => 'post',
                'post_title'  => $request['title'],
                'post_status' => 'publish',
            ) );
        },
        'permission_callback' => function ( $request ) {
            return current_user_can( 'publish_posts' );
        },
        'args'                => array(
            'title' => array(
                'type'              => 'string',
                'required'          => true,
                'validate_callback' => function ( $param, $request ) {
                    if ( ! preg_match( '/[a-z0-9]+/', $param ) ) {
                        return new WP_Error(
                            'rest_invalid_title',
                            'Please enter a valid title for the post.',
                            array( 'status' => 400 )
                        );
                    }

                    return true;
                }
            ),
        ),
    ) );
} );

However, note that if foobar is actually a custom post type, then when registering the post type (see register_post_type()), you could actually set show_in_rest to true and then set rest_controller_class to the name of a custom REST controller class like the one here.