I'll start with the first question question as I think the answer is more straightforward.
- Is there a functionality in Azure AI Search that enables a data storage and index that is user-based and where user-uploaded content can be sent?
Yes, you could design a document index in which one of the attributes is something like index_user_id. You could query your index and only return results with the current user's id. There are several storage options for Azure AI search. For this use case I would use Blob storage based on the file types and metadata you could pass to the search service. For this solution you'd need to build a document intake process, indexing process(AI search indexer), azure OpenAI integration, and WebApp for end user interface.
- How can the content of a user-uploaded document be accessed and used in a RAG system from a deployed Azure AI Studio chatbot?
The deployed AI Studio deploys a boilerplate application to a app service. There are env variables that allow you to connect to an azure search or similar service. If you connect to a data source within the studio you'll be asked for your search service and those env variables will be set on the app service when you select "Deploy to a web App". At that point you'd be able to use whatever your storage solution is to be the "User Uploaded document repository".
Let me know if this helps!
Max