About Ansible, it’s not declarative in the same way Nix is. The way it actually works is it executes little Python programs based on your config. But if you stick to the high level modules, it has a declarative feel. Also, the Python aspect is useful because you can include bits of Python to manage things like generating complicated config files.
I haven’t checked out guix home, but it looks interesting. I have been doing some Lisp recently, so maybe the time is coming.