Thank you Econ Odoo, that helped massively!

Tiny change I made: I ofcourse wanted it to have a id created by Odoo themselves. I just put in 123 as a placeholder. I forgot to say that.

So in the supplier_contact code it should probably direct Odoo to create an ID themselves for the supplier. This is probably sufficiantly managed in the res.partner code. I cannot find a def create in any Res_partner model that makes the ID, but in the Lunch_supplier model it states the following as part of the creating proces of a supplier:

self.env['ir.model.data'].sudo().create([{
    'name': f'lunch_supplier_cron_sa_{cron.ir_actions_server_id.id}',
    'module': 'lunch',
    'res_id': cron.ir_actions_server_id.id,
    'model': 'ir.actions.server',
    # noupdate is set to true to avoid to delete record at module update
    'noupdate': True,
} for cron in crons])
for vals, cron in zip(vals_list, crons):
    vals['cron_id'] = cron.id

To me it seems that the

'res_id': cron.ir_actions_server_id.id,

part initiates Odoo to create an ID.

Which to me meant that if I changed my code to the following:

supplier = self.env['lunch.supplier'].search([('name', '=', 'Vendor123')])
if not supplier:
    supplier_contact = self.env['res.partner'].create({'res_id': cron.ir_actions_server_id.id, 'name': 'Vendor123'})
    supplier = self.env['lunch.supplier'].create({'name': 'Vendor123',
                                                  'partner_id': supplier_contact.id})

However, that gave me the following error:

NameError: name 'cron' is not defined

I am a beginnner, and yes I am creative, so I continued.

Since the id creation is taken care of in the res_partner model, I just skipped the ID part and only listed name as data to help Odoo create. That worked fantastically!

Final working code:

supplier = self.env['lunch.supplier'].search([('name', '=', 'Vendor123')])
if not supplier:
    supplier_contact = self.env['res.partner'].create({'name': 'Vendor123'})
    supplier = self.env['lunch.supplier'].create({'name': 'Vendor123',
                                                  'partner_id': supplier_contact.id})

Thanks for your help again Econ Odoo. I hope someone in the future might learn from my mistakes :)

Partner id is the contact of the Vendor. If you're creating a new Vendor, you're supposed to create a new contact for it first and use that for the vendor creation.

Your code:

supplier_contact = self.env['res.partner'].create({'id': 123, 'name': 'Vendor123'})

This will have the new partner. Then 

 supplier = self.env['lunch.supplier'].create({'name': 'Vendor123',
                                                  'partner_id': supplier_contact.id})

 But reading your code, you seems to be super creative in using variables using just a single variable supplier for everything which may confuse python, Odoo and possibly anyone who are trying to help you here. Be less creative and use a different variable for different thing.