Is there a good book that explains Nix, from theory to real world dev usage?
But IMHO I would try to take a flake centric approach because there's a _ton_ of cruft in the docs about stuff like channels that all gets completely jettisoned and dropped once flakes are the norm. It's just a lot of concepts and CLI commands, flags, rituals, etc. in the docs that will give you nothing of value in a flakes world. Unfortunately there are no real docs that make this clear that the nix world is deep into a major transition and flakes are the clear future.
This 1 page intro to the nix language was all I needed to get comfortable with it too: https://github.com/tazjin/nix-1p It's really a pretty simple data-oriented language when you get down to it.
Yes, if you think of nix-the-language as a bunch of helpers that creates a big key-value JSON object then you will start to get a better mental model.
What were you trying to do such that the way the docs said to do it was wrong?
"package manager" is literally in the first sentence.
Nix does have equivalents to "apt install <package>", etc... but, it's prone to "I forgot I did that / I didn't know I did that", and problems arising from that. (Other distribution package managers like apt-get or pacman require installing packages as root; but with nix packages should be installed as non-root. And the nix command to update installed packages isn't intuitive).
What's typically encouraged is to instead install packages as part of the NixOS configuration, or as part of a home-manager configuration.
Or, just using commands like "nix shell nixpkgs#<package>", which just adds the program to the path in the current shell, without installing it. (Which is a neat feature of nix).