how to add a hidden type input to wp admin login form programmatically

You can hook the login_form action:

/**
 * Fires following the 'Password' field in the login form.
 *
 * @since 2.1.0
 */
do_action( 'login_form' );

which is called between the password box and the ‘remember me?’ checkbox, and write out your hidden input field there, e.g.

function wpse_366921_hidden_login_field() {
    ?>
    <input type="hidden" name="hidden-login-field" value="1" />
    <?php
}
add_action( 'login_form', 'wpse_366921_hidden_login_field', 10, 0 );