Does anyone know a technical term for this? Like describing the Milky Way from within it...

Perhaps a model for explaining the model that explains the model and so on?, that is a recursive procedure to obtain a fixed point for the function f(model) = f(explain(model))? So that f = model0 where model0 is the fixed point of the function f. In order to use explain you should read first Kant's account of Reason (1). Hince knowledge should be expanded within the dialectics framework so that no concept of God or World emerge from it.

(1) https://plato.stanford.edu/entries/kant-reason/#LimiReas

Psychedelics, schizophrenia and other mental illnesses, meditation and other techniques are reasonably valid examples of leaving I'd say. We don't really study them them to the degree that we could, but perhaps some day we will.

Psychedelics, meditation and mental illness show you or change the contents of the house - but you can never leave the house of the existence of consciousness. The closest thing we have to that would be death, and even then you only know if consciousness disappears if you die.

In fact, you would not even experience the disappearance of consciousness - because the consciousness that would experience this has disappeared. It is impossible to experience the absence of consciousness.

They are reputed to be able to pop the delusion of omniscience that accompanies standard consciousness as well.