flake: add Flake Parts tree into testbed environment

Add the Flake Parts tree into the testbed environment, enabling
realistic testing interactions.

Flake Parts is chosen over Stylix to reduce cache invalidations, and
over other flake inputs as the smallest tree.

stylix/testbed/default.nix

@@ -14,6 +14,7 @@ let
 
         modules =
           [
+            (lib.modules.importApply ./modules/flake-parts.nix inputs)
             ./modules/common.nix
             ./modules/enable.nix
             ./modules/application.nix

stylix/testbed/modules/flake-parts.nix

@@ -0,0 +1,7 @@
+inputs:
+{ lib, ... }:
+{
+  home-manager.sharedModules = lib.singleton {
+    home.file.flake-parts.source = inputs.flake-parts;
+  };
+}