Add treefmt formatter (nix fmt + flake check gate)

flake.nix

@@ -1,6 +1,8 @@
 {
   inputs.clan-core.url = "https://git.clan.lol/clan/clan-core/archive/25.11.tar.gz";
   inputs.nixpkgs.follows = "clan-core/nixpkgs";
+  inputs.treefmt-nix.url = "github:numtide/treefmt-nix";
+  inputs.treefmt-nix.inputs.nixpkgs.follows = "nixpkgs";
 
   outputs =
     {
@@ -31,24 +33,36 @@
         "age-plugin-fido2-hmac"
       ];
       };
+
+      systems = [
+        "x86_64-linux"
+        "aarch64-linux"
+        "aarch64-darwin"
+        "x86_64-darwin"
+      ];
+      forAllSystems = nixpkgs.lib.genAttrs systems;
+      pkgsFor = system: clan-core.inputs.nixpkgs.legacyPackages.${system};
+      treefmtFor = system: inputs.treefmt-nix.lib.evalModule (pkgsFor system) ./fmt.nix;
     in
     {
       inherit (clan.config) nixosConfigurations nixosModules clanInternals;
       clan = clan.config;
+
+      # `nix fmt` and the `nix flake check` formatting gate.
+      formatter = forAllSystems (system: (treefmtFor system).config.build.wrapper);
+      checks = forAllSystems (system: {
+        formatting = (treefmtFor system).config.build.check self;
+      });
+
       # Add the Clan cli tool to the dev shell.
       # Use "nix develop" to enter the dev shell.
-      devShells =
-        nixpkgs.lib.genAttrs
-          [
-            "x86_64-linux"
-            "aarch64-linux"
-            "aarch64-darwin"
-            "x86_64-darwin"
-          ]
-          (system: {
-            default = clan-core.inputs.nixpkgs.legacyPackages.${system}.mkShell {
-              packages = [ clan-core.packages.${system}.clan-cli ];
-            };
-          });
+      devShells = forAllSystems (system: {
+        default = (pkgsFor system).mkShell {
+          packages = [
+            clan-core.packages.${system}.clan-cli
+            (treefmtFor system).config.build.wrapper
+          ];
+        };
+      });
     };
 }