So, rather than using Puppet + Debian or something, you would probably just use Guix, because Guix has system configuration tools[0]. Guix (Nix, too) solves system management problems from the bottom, at the systems level. Other tools tack it on top of existing operating systems.
[0] https://www.gnu.org/software/guix/manual/guix.html#System-Co...
This kind of configuration goes one level above package management, whether it's guix, apt, yum, pacman, or anything else.
Edit: you actually said benefits of guix in the original question - it gives you the way to make a localised installation of something you want. Chef/Puppet cannot be it on their own.
It does, actually. Check out the documentation for details:
https://www.gnu.org/software/guix/manual/guix.html#System-Co...
The fun part is that configurations can be treated exactly like packages and vice-versa. A "package" can depend on a specific configuration too. After you realize that package management and configuration management are not really disjoint ideas, it's the only sane way to think about reproducing software reliably.