Where is 'Payment Method' stored in the database for a Contribution "Payment Details"?
The payment method of a contribution table is stored on the civicrm_financial_trxn table. Payments and Contributions are related through civicrm_entity_financial_trxn table.

Some discussions about similar issues have recently taken place on financial issue board. Please consider whether you can make a contribution on any of them or if you need to report a new one.