Turns out I was missing a key step.

Once you've switched your project to using a postgresql DB (essential for Vercel) you will need to run npx prisma migrate deploy from the root of your project in your code editor which will use your defined .env URLs (POSTGRES_URL_NON_POOLING, and POSTGRES_PRISMA_URL) to migrate your tables from your project to the db.

Then you're good to go.