feat: add nix for formatting

Also adds CI tests!

flake.nix

@@ -0,0 +1,43 @@
+{
+  description = "Description for the project";
+
+  inputs = {
+    flake-parts.url = "github:hercules-ci/flake-parts";
+    nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable";
+    treefmt-nix = {
+      url = "github:numtide/treefmt-nix";
+      inputs.nixpkgs.follows = "nixpkgs";
+    };
+    systems.url = "github:nix-systems/default";
+  };
+
+  outputs =
+    inputs@{ flake-parts, ... }:
+    flake-parts.lib.mkFlake { inherit inputs; } {
+      imports = [ inputs.treefmt-nix.flakeModule ];
+      systems = import inputs.systems;
+
+      perSystem =
+        { pkgs, ... }:
+        {
+          # Export pkgs.hello so we can test this action
+          packages = { inherit (pkgs) hello; };
+
+          # Setup formatters
+          treefmt = {
+            # Ignore images
+            settings.global.excludes = [ "*.png" ];
+            projectRootFile = "flake.nix";
+            programs = {
+              mdformat.enable = true;
+              nixfmt.enable = true;
+              shfmt.enable = true;
+              shellcheck.enable = true;
+              statix.enable = true;
+              typos.enable = true;
+              yamlfmt.enable = true;
+            };
+          };
+        };
+    };
+}