Hi! Welcome to the Nix community. You've made an unfortunate choice for your first package, because VPNs usually need to be integrated with system networking to function properly, and Nix without a daemon or NixOS is not able to do that. A distro has multiple pieces, including package management (putting executables and libraries onto your disk) and system configuration (interacting with the low-level hardware). Nix is a package manager; NixOS is Nix and also system configuration and some other stuff like booting.
For the specific case of Mullavad, I found this community documentation:
Warning: Mullvad VPN currently only works if systemd-resolved is enabled.
All you need to know here is that systemd is part of the system configuration; systemd-resolved is part of how some Linux systems look up names. Nix's version of Mullavad VPN is only compatible with a specific NixOS configuration.
Honestly, it's great to hear that the GUI and nix-env are working for you; those are things that often break on unusual targets. It sounds like the only thing that doesn't work is something which cannot work as installed.