Azure Speech does not retain or store the data provided by customers when using real-time Speech-to-Text, pronunciation assessment, and speech translation. In batch transcription, customers specify their own storage locations to send the audio input. Generated transcription text may be stored either in the customer’s own storage or Microsoft storage if no storage is specified. If output transcriptions are stored in Microsoft storage, Customers may delete the data either by calling a deletion API or setting the timeToLive parameter to automatically delete the data in a specified time.
https://learn.microsoft.com/en-us/answers/questions/115152/data-stored-by-azure-speech
In the case of cognitive services that store customer data, you have full control over the storage and deletion of any customer data that the cognitive services store as part of providing the services to you. For cognitive services that do not store customer data, the customer data is automatically deleted after processing
In the specific context of using Azure Speech with an API key and screen readers in a third-party software, it is likely that your texts or audio files are not stored or logged in Azure, especially if you're using real-time services. However, this might depend on the specific implementation of the third-party software. For a definitive answer, you may need to consult with the third-party software provider or conduct a specific search regarding the software's interaction with Azure Speech..