No, the human user doesn't have permissions, the LLM system has permissions, we create a user for the process, we've been doing this since unix, take a look at what your HTTP server runs as. There's no deputization of permissions going on here, at least on my systems.
Even if there are user-level permissions, you then use a role-based approach (SQL user for a type of users, for example accountant, manager, etc..) and restrict its permissions accordingly, I don't think the idea of restricting permissions so that we avoid users fucking the database up is new.
Many organizations have DBA whose role it is to convert user queries into SQL queries, Juniors usually have tighter permissions. Also non-technical managers and analysts can have access to the database.
As I said, not a new problem, SQL servers have mature permission systems.
If that is not enough, just write an API wrapper. It's what Amazon does anyways, Bezos' memo explicitly states that teams should not expose databases, rather they should expose APIs, under punishment of firing.