refactor: create a new nix formatter run command alias for nix fmt

This refactor shouldn't change much except add a new `nix formatter run`
command. This creates space for the new `nix formatter build` command,
which I'll be introducing in the next commit.

tests/functional/formatter.sh

@@ -0,0 +1,38 @@
+#!/usr/bin/env bash
+
+source common.sh
+
+TODO_NixOS # Provide a `shell` variable. Try not to `export` it, perhaps.
+
+clearStoreIfPossible
+rm -rf "$TEST_HOME"/.cache "$TEST_HOME"/.config "$TEST_HOME"/.local
+
+cp ./simple.nix ./simple.builder.sh ./fmt.simple.sh "${config_nix}" "$TEST_HOME"
+
+cd "$TEST_HOME"
+
+nix fmt --help | grep "forward"
+
+cat << EOF > flake.nix
+{
+  outputs = _: {
+    formatter.$system =
+      with import ./config.nix;
+      mkDerivation {
+        name = "formatter";
+        buildCommand = ''
+          mkdir -p \$out/bin
+          echo "#! ${shell}" > \$out/bin/formatter
+          cat \${./fmt.simple.sh} >> \$out/bin/formatter
+          chmod +x \$out/bin/formatter
+        '';
+      };
+  };
+}
+EOF
+# No arguments check
+[[ "$(nix fmt)" = "Formatting(0):" ]]
+# Argument forwarding check
+nix fmt ./file ./folder | grep 'Formatting(2): ./file ./folder'
+nix flake check
+nix flake show | grep -P "package 'formatter'"