> it was just moved one step further down the layer
And therefore, crucially, you don't need to manage it yourself anymore. The only thing you need to do is tell the system what to index (which is code, not state/data).
You do manage the state of your database. When you do an UPDATE, you explicitly change the state.
The statefulness of an index, however, is merely an implementation detail. A database without indices would be in the same state, and behave the same (except much slower). This means that the state is not important for the semantics of the datastore, unlike with a regular database.
And therefore, crucially, you don't need to manage it yourself anymore. The only thing you need to do is tell the system what to index (which is code, not state/data).