Adding menu item to WordPress admin bar for editors to edit one plugin’s settings

I have read the about this function and I see you need to parameter capability to allows the user can see the menu as an admin or editor.

Read more the function to know detail: https://developer.wordpress.org/reference/functions/add_menu_page/

And you can try this the following code.

/**
 * Register menu for settings form page.
 */
public function register_menu() {
    // Add top level menu page.
    add_menu_page(
        __('Siteimprove Plugin'),
        __('Siteimprove'),
        'edit_posts',//change this line 'manage_options' to 'edit_posts'
        'siteimprove',
        'Siteimprove_Admin_Settings::siteimprove_settings_form'
    );
}

I hope it works for you. Good luck!