Linux

it uses a weird combination of your system libraries, installing its own libraries into your system on its own without informing your primary package manager, and using some specific library versions separate from your system libraries for some apps.

That is not at all true.

There is one explicit case where "system libraries" are used by Nix programs and that is graphics drivers. This is not done outside of NixOS as it does not trivially work there; it's still an open problem. We can discuss about the reasons for this impurity's existance and its intricacies but all that is important here that this impurity is the sole exception, not the norm.

Apart from that, Nix will never under any circumstances load (much less modify) libraries of any kind from any global path; system-controlled, user-controlled or otherwise. That'd be contrary to the fundamental principles of Nix.

It will always use "specific library versions separate from your system libraries" aka. the explicitly and exhaustively precisely declared dependencies in the Nix store. That's the whole point of it.

I'd recommend you read up on Nix again and revise your opinion once you understand what it actually does because it's clear that whatever source you had for information on Nix was entirely wrong.