Currently I use Ansible to deploy my dotfiles, along with anything else needed to setup a workstation. I keep seeing people mention Nix. Would it give me anything that Ansible and Git can't give me?

Mostly it provides guarantees about your system. It guarantees that anything not in your config is not on your system (for the most part). It guarantees that everything builds successfully before it applies any changes. Most of the filesystem is immutable so it forces you to use the configuration.

There are some other advantages: rollback to a previous state at any time, enable complex system services with one line in your config file, install multiple versions of tools on your system without conflicts, install programs without root (using home manager), build VMs and Docker images, pin the versions and dependencies of all packages for reproducibility, patch software with your own tweaks natively. You can also put a Nix file in a code repo and easily share your build dependencies with other developers.