Give REST API authentication a lower priority

Bigger than add_filter( 'determine_current_user', 'wp_validate_auth_cookie' );
Smaller than add_filter( 'determine_current_user', 'wp_validate_logged_in_cookie', 20
);

This solve issues while trying to authenticate in a browser while logged
in.

Closes #13134

includes/api/class-wc-rest-authentication.php

@@ -18,7 +18,7 @@ class WC_REST_Authentication {
 	 * Initialize authentication actions.
 	 */
 	public function __construct() {
-		add_filter( 'determine_current_user', array( $this, 'authenticate' ), 100 );
+		add_filter( 'determine_current_user', array( $this, 'authenticate' ), 15 );
 		add_filter( 'rest_authentication_errors', array( $this, 'check_authentication_error' ) );
 		add_filter( 'rest_post_dispatch', array( $this, 'send_unauthorized_headers' ), 50 );
 	}