Hi,

You can add a new field in the tree view to display the barcode in the tree view. Either you can do it by creating custom addons or from manually editing after the user interface.

If you want to do it from the UI, activate the developer mode and open the products list view, then click on lady debugger button near the logged in user name in the menu bar, and select the Edit List View as shown in above image,

Then add a line in the position you required, <field name="barcode"/>

UPDT:

To add the custom field to the sale order line, first, you can inherit the model and add the field to the model,

class SaleOrderLine(models.Model):
    _inherit = 'sale.order.line'

    barcode = fields.Char(string='Product Barcode')

Then in the XML,'

<record id="sale_order_view_inherit_barcode1" model="ir.ui.view">
    <field name="name">sale.order.form.inherit</field>
    <field name="model">sale.order</field>
    <field name="inherit_id" ref="sale.view_order_form"/>
    <field name="arch" type="xml">
       <xpath expr="//field[@name='order_line']/tree/field[@name='product_id']" position="after">
                <field name ="barcode"/>
       </xpath>
    </field>
</record>

Also, already we have the product_id field in the order line, you can remove the one of the field barcode_id you have defined and change the other field as follows,

barcode = fields.Char(related='product_id.barcode', string="Product Barcode", store=True).

Thanks