Search WordPress using static html page

If you want to submit a form you need a <form> element to contain the input. (You can get away without one but you’d need script to fake the submit.) The action is the homepage with the search text in an input named ‘s’, e.g.

<form method="get" action="https://example.com/">
    <input type="search" name="s" />
    <input type="submit" value="Search" />
</form>

for a bare-bones form. Or you can use get_search_form() to get a version with all of the ARIA attributes set up too.