Behavior: Starts a new payment transaction by communicating with the configured merchant processor. This should be called when the user is most likely going to be making the transaction. The Cognito contact ID is extracted from the authenticated user's claims.

Authorization: Requires an authenticated user (class-level [Authorize]). The user's Cognito contact ID claim is required.

Side Effects: A new payment transaction is initiated with the merchant processor. The transaction state is persisted for subsequent cancel or complete operations.

Error Scenarios: Returns 400 if the request model is invalid or the Cognito contact ID claim is missing. Returns 401 if the user is not authenticated.