Is there a dedicated payee/vendor field available in the account register in GnuCash?

Reminder: This answer has not been generated by AI tools.

[…] trying to figure out where one enters the vendor/payee detail for a given transaction.

To associate a transaction with a vendor or customer you have to use the Process Payments dialog. The Process Payments dialog is accessible via the Business menu in each of the Customer, Vendor and Employee submenus. That means, to use the Process Payments dialog you have to use the business features – issuing invoices, recordings bills, etc. – too.

Is there no such dedicated field, are you really just limited to a date, number, description/memo, transaction type, and amount?

Yes/no: Yes, transactions can have vendor/payee information associated with them. No, other than via Process Payments dialog you cannot edit this information.

[…] establish some kind of vendor prefix in their memos to be able to do vendor oriented reports?

No, the Reports do not allow to filter based on some character string. You need structured information such as accounts or vendors/customers.

How exactly do people track vendor/payee/merchant details in GnuCash?

People who want that kind of detail use the business features. It is not just “some business to business invoicing feature”, this is the way to go. In GnuCash you account based on what reports you want to generate: as a private individual you may be happy to see what you spend your money on.