It doesnt' have to be REST, but it does have to prevent the LLM from having access to data you wouldn't want the user having access to. How exactly you accomplish that is up to you, but the obvious way would be to have the LLM use the same APIs you would use to implement a UI for the data (which would typically be REST or some other RPC). The ability to run SQL would allow the LLM to do more interesting things for which an API has not been written, but generically adding auth to arbitrary sql queries is not a trivial task, and does not seem to have even been attempted here.

RLS is the answer here -- then injection attacks are confined to the rows that the user has access to, which is OK.

Performance attacks though will degrade the service for all, but at least data integrity will not be compromised.