This has been happening for years, long pre-dating LLMs or the current AI hype. There are a huge number of companies in the medical transcription space.

Some are software companies that ingest data to the cloud as you say. Some are remote/phone transcription services, which pass voice data to humans to transcribe it. Those humans then store it in the cloud when it is returned to a doctor's office. Some are EMR-integrated transcription services which are either cloud-based with the rest of the EMR or, for on-premise EMRs, ship data to/from the cloud for transcription.