fix(routines): enforce min_interval_hours and minoxidil flag server-side

Two bugs in /routines/suggest where the LLM could override hard constraints:

1. Products with min_interval_hours (e.g. retinol at 72h) were passed to
   the LLM even if used too recently. The LLM reasoned away the constraint
   in at least one observed case. Fix: added _filter_products_by_interval()
   which removes ineligible products before the prompt is built, so they
   don't appear in AVAILABLE PRODUCTS at all.

2. Minoxidil was included in the available products list regardless of the
   include_minoxidil_beard flag. Only the objectives context was gated,
   leaving the product visible to the LLM which would include it based on
   recent usage history. Fix: added include_minoxidil param to
   _get_available_products() and threaded it through suggest_routine and
   suggest_batch.

Also refactored _build_products_context() to accept a pre-supplied
products list instead of calling _get_available_products() internally,
ensuring the tool handler and context text always use the same filtered set.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/tests/test_routines_helpers.py

@@ -15,6 +15,7 @@ from innercontext.api.routines import (
     _ev,
     _extract_active_names,
     _extract_requested_product_ids,
+    _filter_products_by_interval,
     _get_available_products,
     _is_minoxidil_product,
 )
@@ -204,9 +205,8 @@ def test_build_products_context(session: Session):
     session.add(s)
     session.commit()
 
-    ctx = _build_products_context(
-        session, time_filter="am", reference_date=date.today()
-    )
+    products_am = _get_available_products(session, time_filter="am")
+    ctx = _build_products_context(session, products_am, reference_date=date.today())
     # p1 is medication but not minoxidil (wait, Regaine name doesn't contain minoxidil!) -> skipped
     assert "Regaine" not in ctx
 
@@ -215,9 +215,8 @@ def test_build_products_context(session: Session):
     session.add(p1)
     session.commit()
 
-    ctx = _build_products_context(
-        session, time_filter="am", reference_date=date.today()
-    )
+    products_am = _get_available_products(session, time_filter="am")
+    ctx = _build_products_context(session, products_am, reference_date=date.today())
     assert "Regaine Minoxidil" in ctx
     assert "Sunscreen" in ctx
     assert "inventory_status={active:2,opened:1,sealed:1}" in ctx
@@ -375,6 +374,106 @@ def test_extract_active_names_uses_compact_distinct_names(session: Session):
     assert names == ["Niacinamide", "Zinc PCA"]
 
 
+def test_get_available_products_excludes_minoxidil_when_flag_false(session: Session):
+    minoxidil = Product(
+        id=uuid.uuid4(),
+        name="Minoxidil 5%",
+        category="hair_treatment",
+        is_medication=True,
+        brand="Test",
+        recommended_time="both",
+        leave_on=True,
+        product_effect_profile={},
+    )
+    regular = Product(
+        id=uuid.uuid4(),
+        name="Cleanser",
+        category="cleanser",
+        brand="Test",
+        recommended_time="both",
+        leave_on=False,
+        product_effect_profile={},
+    )
+    session.add_all([minoxidil, regular])
+    session.commit()
+
+    # With flag True (default) - minoxidil included
+    products = _get_available_products(session, include_minoxidil=True)
+    names = {p.name for p in products}
+    assert "Minoxidil 5%" in names
+    assert "Cleanser" in names
+
+    # With flag False - minoxidil excluded
+    products = _get_available_products(session, include_minoxidil=False)
+    names = {p.name for p in products}
+    assert "Minoxidil 5%" not in names
+    assert "Cleanser" in names
+
+
+def test_filter_products_by_interval():
+    today = date.today()
+
+    p_no_interval = Product(
+        id=uuid.uuid4(),
+        name="No Interval",
+        category="serum",
+        brand="Test",
+        recommended_time="both",
+        leave_on=True,
+        product_effect_profile={},
+    )
+    p_interval_72 = Product(
+        id=uuid.uuid4(),
+        name="Retinol",
+        category="serum",
+        brand="Test",
+        recommended_time="pm",
+        leave_on=True,
+        min_interval_hours=72,
+        product_effect_profile={},
+    )
+    p_interval_48 = Product(
+        id=uuid.uuid4(),
+        name="AHA",
+        category="exfoliant",
+        brand="Test",
+        recommended_time="pm",
+        leave_on=True,
+        min_interval_hours=48,
+        product_effect_profile={},
+    )
+
+    last_used = {
+        str(p_interval_72.id): today - timedelta(days=1),  # used yesterday -> need 3 days
+        str(p_interval_48.id): today - timedelta(days=3),  # used 3 days ago -> 48h ok
+    }
+
+    products = [p_no_interval, p_interval_72, p_interval_48]
+    result = _filter_products_by_interval(products, today, last_used)
+    result_names = {p.name for p in result}
+
+    assert "No Interval" in result_names  # always included
+    assert "Retinol" not in result_names  # used 1 day ago, needs 3 -> blocked
+    assert "AHA" in result_names  # used 3 days ago, needs 2 -> ok
+
+
+def test_filter_products_by_interval_never_used_passes():
+    today = date.today()
+    p = Product(
+        id=uuid.uuid4(),
+        name="Retinol",
+        category="serum",
+        brand="Test",
+        recommended_time="pm",
+        leave_on=True,
+        min_interval_hours=72,
+        product_effect_profile={},
+    )
+    # no last_used entry -> should pass
+    result = _filter_products_by_interval([p], today, {})
+    assert len(result) == 1
+
+
 def test_product_details_tool_handler_returns_product_payloads(session: Session):
     p = Product(
         id=uuid.uuid4(),