Yeah it gave me this hunch too.

I could imagine a language /framework where we declare the schema of data, indexes on this schema, and either let a query planner optimise data access or explicitly specify which index to use

You've described SQL :)

Sure at a conceptual level all stored data, even transitory, is a database, but I don't think that's a helpful analysis here, for a start current databases are far too limited.

A database implies a separate runtime system to manage data, whereas this is data storage within a program, part of 'data-structures and algorithms'.

Sure, but you're describing a fully functional database integrated with a fully functional programming language.

Just because you're describing a possibly novel integration of those two systems doesn't mean it's not valuable to consider the prior art for both constituent pieces.