Hi,

You can try like below.

Inherit the model stock.picking and super the function of button validate

from odoo.tests import Form

class StockPicking(models.Model):
    _inherit = 'stock.picking'
    
    def button_validate(self):
        res = super(StockPicking, self).button_validate()
        label_print_from = Form(self.env['product.label.layout'].with_user(user),
                                view='stock.product_label_layout_form_picking')
        label_print_from.picking_quantity = 'custom'
        label_print_from.custom_quantity = 1
        label_print_from.print_format = 'zpl'
        label_print_from.product_ids = self.product_id
        label_id = label_print_from.save()
        label_id.process()
    
        return res

Using this method you may able to print barcode while click on validate button.

Regards