Here is my first solution. I'm pretty sure that you won't like it. I give all comments/improvements with great pleasure.

I'm very excited to read what you will have to say about this code...

Thanks

class AccountInvoiceLine(models.Model):
    _inherit = "account.invoice.line"

    pack_operation = fields.Many2one(comodel_name='stock.pack.operation', compute='compute_stock_pack_operation_id')
    
    @api.one
    def compute_stock_pack_operation_id(self):
        procurement_order_obj = self.env['procurement.order']
        stock_operation_obj = self.env['stock.pack.operation']
        all_picking_ids_for_this_invoice_line = []
        
        for saleorderline in self.sale_line_ids:
            for procurement in saleorderline.procurement_ids:
                for stockmove in procurement.move_ids:
                    if stockmove.picking_id.id not in all_picking_ids_for_this_invoice_line:
                        all_picking_ids_for_this_invoice_line.append(stockmove.picking_id.id)
                                                                                                            
 
        stock_operation = stock_operation_obj.search(
            [ '&',
                                ('picking_id','in',all_picking_ids_for_this_invoice_line),
                ('product_id','=',self.product_id.id)                                ]            )
                                     
        self.pack_operation = stock_operation[0]