Assert the page offers a search form: the Search block on a block theme, searchform on a classic theme.
Examples
Then I should see the search form
And we should see a search form
Then should see the search form
Then I should not see the search form
But we should not see a search form
Pattern
Then(/^(I |we )*should( not)* see (?:a|the) search form$/, …)
Part of @webship-js/wordpress-steps (github.com/webship/wordpress-steps), a step pack for Webship-js 2.0.x.