Assert the HTTP status the *current session* gets for the current page, by re-requesting it through the browser context's own cookie jar.
webship-js's "the response status code should be" re-requests without the session cookies, so it always answers as an anonymous visitor; use that for public pages and this one when the answer depends on who is logged in (an editor's 403 on /admin/people, an administrator's 200 on the same page).
Examples
Then the page should return HTTP status 200
And the page should return HTTP status 403
Then the current page should return status 404
And the page should not return HTTP status 500
Then the page should respond with status code 200
Pattern
Then(/^(?:the )?(?:current )?page should( not)* (?:return|respond with) (?:HTTP |http )?status(?: code)? (\d+)$/, …)
Part of @webship-js/drupal-core-steps (github.com/webship/drupal-core-steps), a step pack for Webship-js 2.0.x.