Which DML operations are NOT supported through the SOAP API?

The correct answer points to the fact that the SOAP API in Salesforce does not support batch operations, which include executing bulk actions on multiple records at once. The SOAP API is designed for individual record manipulations through direct calls for create, delete, retrieve, and update operations.

Batch operations typically have their own mechanisms, such as the Bulk API, which is optimized for handling large quantities of records and operates through batches. The SOAP API is mainly synchronous and should be used for transaction-level operations, meaning that it is intended for processing a single request at a time, fitting many cases where immediate responses are necessary but not for bulk processing.

In contrast, the other options involve individual variations of data manipulation language (DML) operations that are indeed supported by the SOAP API, allowing for creating, retrieving, updating, and deleting records within its synchronous architecture. Therefore, the limitation of the SOAP API regarding batch processing is what makes the option of batch and execute the correct choice here.