feat(flake): switch to treefmt-nix

This allows me to remove all checks and replace them with treefmt-nix

flake-modules/checks.nix

@@ -1,26 +0,0 @@
-{ lib, ... }:
-{
-  perSystem =
-    { pkgs, self', ... }:
-    {
-      checks =
-        let
-          src = builtins.path {
-            path = ../.;
-            name = "configuration.nix";
-          };
-          runCmdInSrc =
-            name: cmd:
-            pkgs.runCommandNoCC name { } ''
-              cd ${src}
-              ${cmd}
-              mkdir $out
-            '';
-        in
-        {
-          fmt = runCmdInSrc "fmt-src" "${lib.getExe self'.formatter} --check .";
-          lint = runCmdInSrc "lint-src" "${lib.getExe pkgs.statix} check .";
-          typos = runCmdInSrc "typos-src" "${lib.getExe pkgs.typos} .";
-        };
-    };
-}

flake-modules/default.nix

@@ -4,7 +4,8 @@ let
 in
 {
   imports = [
-    ./checks.nix
+    inputs.treefmt-nix.flakeModule
+
     ./devshells.nix
     ./docs.nix
     ./example-vm.nix
@@ -15,11 +16,19 @@ in
   ];
 
   perSystem =
-    { system, pkgs, ... }:
+    { system, ... }:
     {
       _module.args.pkgs = import inputs.nixpkgs { inherit system overlays; };
 
-      # Nix files formatter (run `nix fmt`)
-      formatter = pkgs.nixfmt-rfc-style;
+      # Setup formatters
+      treefmt = {
+        projectRootFile = "flake.nix";
+        programs = {
+          nixfmt.enable = true;
+          rustfmt.enable = true;
+          statix.enable = true;
+          typos.enable = true;
+        };
+      };
     };
 }