Shopify has deprecated the processing_method field and it has been removed from the 2023-04 version of the REST Admin API.

Unfortunately, there's no exact replacement for this field in other endpoints.

One field that may be worth checking as a potential alternative is the payment_gateway_names field.

There may also be other fields we can use from the Transaction data that might be close enough (which varies depending on the gateway). Feel free to contact us if you need assistance digging into the Transaction data to see which available fields we may be able to use as an alternative.