I do not think you can force a unique string anywhere in Airtable. You could set your primary field as a formula and set it to record_ID() which should be unique for your base.

If you want a unique primary field that is not meaningful, you can use an autonumber field, or a formula field that include the RECORD_ID().

If you want meaningful primary field, Airtable will not enforce uniqueness. You can set the summary value for the field to show the % unique if you want to check for uniqueness.