Yes, Odoo used to have an option to indicate that a contact was a customer or a vendor (supplier), but that was removed in Odoo 13.

Now there are two hidden fields for customer ranking and supplier ranking.  If you create a new vendor in the Purchase app, the vendor ranking is set to to 1.

You certainly don't need to add the contact twice as a customer and separately as a vendor.  In fact, you can use any contact as a customer or a vendor regardless of the customer ranking / vendor ranking.

But if you do want to set a contact as both a customer and a vendor it's easy to create a Server Action.