Hi Michael,

Yes and no. You can do it partially with Odoo studio but you will also need to use other technical features from Odoo to create this. The closest you would get with Odoo studio itself is by creating a related field to Contact > Tags > Display name but this would only work for one tag. 

As the tags field on a contact can contain multiple records you'll need to first create a many2many field (to the model res.partner.category) with Odoo studio and set the widget "tags" on this new field. The next step is to create an automated action (from Settings > Automation > Automated actions). In this automated action you should set the model "sale.order" and the trigger condition on "Based on Form Modification". You can then set the field which should be watched when changed - which is the equivalent of @api.onchange for a developer - in the "On Change Fields" field. Finally set the "Action to do" field to "Execute Python Code". In this field we can now write Python code to set the labels from the partner if there are any, otherwise we'll set it to False. The Python code should look like this:

if record.partner_id.category_id:
    # Will set all tags from the customer on the field x_studio_field_ul4O7                                          
    record.write({
        'x_studio_field_Ul4P7': [(6, 0, record.partner_id.category_id.ids)]
    })
else:
    record.write({
        'x_studio_field_Ul4P7': False
    })

Your result should look like this:
https://imgur.com/0jLEpo3

After changing to a partner which has a label on the sale order you'll see they are automatically set:
https://imgur.com/IEQxhTs

P.S: Sorry for the image links but posting images has been broken for weeks in the Odoo forum. I've got an official Odoo ticket open for it but it is taking a while. I'll try to update this once it is fixed.

Regards,
Yenthe