Cook the potatoes: Place the baby potato halves in a large pot of salted boiling water. Cook until fork-tender, about 12–15 minutes. Drain well and transfer the potatoes to a large mixing bowl. Allow them to cool slightly.
Make the cream cheese dressing: In a medium bowl, whisk together the softened cream cheese, Greek yogurt, mayonnaise, lemon juice, Dijon mustard, dill, salt, and black pepper until smooth and creamy. Adjust thickness of dressing with water if needed.
Add the remaining ingredients: Add the cream cheese dressing, red onion, capers, and fresh dill, to the bowl with the cooled potatoes. Gently stir until the potatoes are evenly coated.
Finish the salad: Transfer the potato salad to a serving bowl and top with the smoked salmon and more fresh dill. Serve immediately or refrigerate until ready to serve.