How to programmatically append a Paragraph to another Paragraph?

I have a node (e.g. a business "company") with a paragraph referenced field (suppose business "sector", with multiple fields). This paragraph has in its fields a reference to another paragraph (suppose "employee" with multiple fields, one of this is a reference to a taxonomy term). In a hook_form_submit(), with $form and FormStateInterface $form_state as parameters, I need to programmatically associate multiple employees paragraph to a sector paragraph.

...
$node = Node::load($id);
$sector = Paragraph::load($node->get('field_sector')->target_id);

/**
 * List of taxonomy terms loaded elsewhere.
 * I've added a custom elment to the select with "_all" employees
 * in order to associate programmatically all the employees to the $sector.
 * 
 * @var array $employees
 */
foreach ($employees as $employee) {
    $paragraph = Paragraph::create([
        'type' => 'employee',
    ]);
    $paragraph->set('field_name', $employee->get('field_name')->value);
    $paragraph->set('field_age', $employee->get('field_age')->value);
    ...
    $paragraph->save();

    $sector->set('field_employee', $paragraph); // here I don't know how to append to the sector
    $sector->save();
}

I tried to associate each $employee to the $sector but with $sector->set('field_employee', $paragraph); syntax or with $sector->appendItem($paragraph), that works for nodes, it doesn't work.

Is there a way to programmatically add one paragraph to another?

Visualizing the question, in the image below, when I save the entity with custom option "All employees" (_all) selected, I'd like to attach all the 4 paragraph employees associated to the "a selected sector" paragraph (removing _all).

Thanks in advance.

EDIT 1

I saw the suggested answer Programmatically append multiple paragraphs to entity reference field on node but it resolve how to attach a Paragraph to a $node, not a Paragraph to a Paragraph of the $node.

I've try also this:

$employee->setParentEntity($sector, 'field_of_reference');
$employee->save();

but still does not append the $employee to the $sector.

EDIT 2

I've try to follow the suggested posts but I can't figure how to adapt that code inside a hook_form_submit().

Thanks anyway to all, I think its a bad construction on my code.

The problems start with how you load the paragraph. You can't load it like a stand-alone entity:

$sector = Paragraph::load($node->get('field_sector')->target_id);

Instead load it via the reference field:

$sector = $node->get('field_sector')->entity;

Then you can add newly created paragraphs without saving, also nested ones, and when you are ready you can save the parent entity.

See Create nested paragraphs programmatically