@John M Thanks for your patience on this.
I have checked with Azure Cognitive Service engineering team and sharing the below.
The key will be stored in the backend and will only be used by the indexer. It is not displayed for security reasons.
Additionally, if you attempt to retrieve the skillset details using the (Get Skillset) REST API, no keys will be returned in any GET calls to address a security vulnerability.
This behavior is documented in the API versions of Search REST APIs on the Azure AI Search | Microsoft Learn website.
Hope this helps, let me know if you have any further questions on this.