Unapproved events are visible only to the admin. Users don't see them.

Are those events created from the front-end?

I've written small extension that will add additional tab (Approve Status) in the admin add/edit event page with which you can set approval status.

Place the code in your theme/child-theme functions.php file.

add_action('stec_admin_addedit_event_tab', function() {
    printf('<li data-tab="approval">Approve Status</li>');
});
add_action('stec_admin_addedit_event_tab_content', function($event) {
    $status = isset($event) ? $event->get_approved() : 0;
    echo '<div class="stachethemes-admin-section-tab" data-tab="approval">';
    echo '<p class="stachethemes-admin-info">Approval Status</p>';
    echo '<select class="stachethemes-admin-select" name="is_approved">';
    printf('<option %s value="%d">%s</option>', (0 === $status ? 'selected' : ''), 0, esc_html__('Unapproved'));
    printf('<option %s value="%d">%s</option>', (1 === $status ? 'selected' : ''), 1, esc_html__('Approved'));
    echo '</select>';
    echo '</div>';
});
add_filter('stec_insert_post', function($data) {
    if ($data['post_type'] !== 'stec_event') {
        return $data;
    }
    if (filter_input(INPUT_GET, 'task', FILTER_DEFAULT) === 'approve') {
        return $data;
    }
    $approved = filter_input(INPUT_POST, 'is_approved', FILTER_VALIDATE_INT);
    $data['meta_input']['approved'] = $approved;
    return $data;
});

We'll add this functionality by default in the next update.

When events are modified you will have to purge the cache manually from the Cache menu.

It's nuisance. I'll add optional auto-purge option in the cache menu in future update.