feat(backend): include last-used date in product LLM details

backend/tests/test_products_helpers.py

@@ -154,3 +154,24 @@ def test_shopping_tool_handlers_return_payloads(session: Session):
     assert details["products"][0]["inci"] == ["Water", "Niacinamide"]
     assert details["products"][0]["actives"][0]["name"] == "Niacinamide"
     assert "context_rules" in details["products"][0]
+    assert details["products"][0]["last_used_on"] is None
+
+
+def test_shopping_tool_handler_includes_last_used_on_from_mapping(session: Session):
+    product = Product(
+        id=uuid.uuid4(),
+        name="Mapped Product",
+        brand="Brand",
+        category="serum",
+        recommended_time="both",
+        leave_on=True,
+        product_effect_profile={},
+    )
+
+    payload = {"product_ids": [str(product.id)]}
+    details = build_product_details_tool_handler(
+        [product],
+        last_used_on_by_product={str(product.id): date(2026, 3, 1)},
+    )(payload)
+
+    assert details["products"][0]["last_used_on"] == "2026-03-01"