Nix-the-language is isomorphic to JSON, which makes a lot more sense than clinging to some outdated 1970's legacy.
Syntax-wise it's about as similar to JSON as Erlang expressions are (i.e. superficially similar in some cases).
Semantics-wise I've personally found any superficial similarity to JSON to be actively unhelpful in understanding because of some important processing differences (e.g. paths, laziness).
That aside, Nix allows you to create infinite datastructures, e.g.
$ nix eval --expr 'rec { z = { a = z; i = 5; }; }.z.a.a.a.i'
5
But even if JSON did have some way of handling datastructure 'loops', it's still not helpful because of laziness. You almost never want to eagerly evaluate a Nix expression to produce what you seem to term 'Nix data', because you'll invoke the `derivation` built in function to create paths you never actually reference - this is why laziness is such an important property of Nix.
So I'm still not clear what user-facing part of Nix is isomorphic to JSON. If it's just "Nix types [0] are similar to JSON types" then...sure.