A method to provide full management of form submissions to less-privileged WP roles.

access-to-elementor-form-submissions.php

<?php
/*
Plugin Name: Elementor form submission access
Description: Promotes the Elementor Pro form submissions page to top level, and bypasses the excessive and inflexible restrictions on access.
Version: 2.0.0
Author: Some netizen
Update URI: do-not-auto-update
*/

namespace Elementor\Core\Admin\Menu;

defined('ABSPATH') or die;

/**
 * Shim the WordPress submenu function by creating a namespaced version that only exists when Elementor creates its
 * menu items. That means it can intercept the form submissions link to promote it to the top level but other plugins
 * and WordPress code do not see this shimmed version.
 */
function add_submenu_page($parent_slug, $page_title, $menu_title, $capability, $menu_slug, $callback = '', $position = null) {
	if ($menu_slug === 'e-form-submissions') {
		return \add_menu_page($page_title, $menu_title, 'etor_submissions_read', $menu_slug, $callback, 'dashicons-forms', 3.5);
	}
	return \add_submenu_page($parent_slug, $page_title, $menu_title, $capability, $menu_slug, $callback, $position);
}

/**
 * Wait till elementor has registered its REST endpoints, and replace the permissions check with capabilities you can
 * assign to whoever you need, instead of Elementor's use of the generic 'manage_options' capability.
 */
add_filter(
	'rest_endpoints',
	function($endpoints) {
		$permission_callback = function($request) {
			if ($request->get_method() === 'GET') {
				return current_user_can('etor_submissions_read');
			}
			return current_user_can('etor_submissions_full_management');
		};
		foreach ($endpoints as $route => $handlers) {
			if (preg_match('#^/elementor/v1/form(?:-submission)?s(?:$|/)#', $route)) {
				if (!isset($handlers['callback'])) {
					foreach ($handlers as $i => $handler) {
						if (isset($handler['permission_callback'])) {
							$endpoints[$route][$i]['permission_callback'] = $permission_callback;
						}
					}
				}
				elseif (isset($handlers['permission_callback'])) {
					$endpoints[$route]['permission_callback'] = $permission_callback;
				}
			}
		}
		return $endpoints;
	},
	444444444
);