I was curious whether you were using "API" as shorthand for something like "HTTP API" or something like that. It seeemed odd for you to say "Granted, if SQL were directly an API, then GraphQL wouldn't hold too much value" when you actually can use SQL directly in this sense. The reasons that people generally don't are interesting in their own right.
(If I recall - one of the criticisms of GraphQL is that it's a bit too close to actually just exposing your database in this way)
You can implement a GraphQL service in anyway you desire. There is no inherent relation to the storage solution you use.
GraphQL isn't anywhere close to being similar to SQL, so I find the desire for an analogy very confusing.
To me, these are grammars for interacting with an API, not an API.
To me, it is like calling a set of search parameters in a URL an API or describing some random function call as an API. The interface is described by the language. The language isn't the interface.
(If I recall - one of the criticisms of GraphQL is that it's a bit too close to actually just exposing your database in this way)