feat: Merge integrations if a patch or any of its dependencies need them

lib/services/patcher_api.dart

@@ -87,10 +87,21 @@ class PatcherAPI {
         .toList();
   }
 
+  bool dependencyNeedsIntegrations(String name) {
+    return name.contains('integrations') ||
+        _patches.any(
+          (patch) =>
+              patch.name == name &&
+              (patch.dependencies.any(
+                (dep) => dependencyNeedsIntegrations(dep),
+              )),
+        );
+  }
+
   Future<bool> needsIntegrations(List<Patch> selectedPatches) async {
     return selectedPatches.any(
       (patch) => patch.dependencies.any(
-        (dep) => dep.contains('integrations'),
+        (dep) => dependencyNeedsIntegrations(dep),
       ),
     );
   }