feat(profile): add profile settings and LLM user context

backend/tests/test_llm_profile_context.py

@@ -0,0 +1,23 @@
+from datetime import date
+
+from sqlmodel import Session
+
+from innercontext.api.llm_context import build_user_profile_context
+from innercontext.models import SexAtBirth, UserProfile
+
+
+def test_build_user_profile_context_without_data(session: Session):
+    ctx = build_user_profile_context(session, reference_date=date(2026, 3, 5))
+    assert ctx == "USER PROFILE: no data\n"
+
+
+def test_build_user_profile_context_with_data(session: Session):
+    profile = UserProfile(birth_date=date(1990, 3, 20), sex_at_birth=SexAtBirth.FEMALE)
+    session.add(profile)
+    session.commit()
+
+    ctx = build_user_profile_context(session, reference_date=date(2026, 3, 5))
+    assert "USER PROFILE:" in ctx
+    assert "Age: 35" in ctx
+    assert "Birth date: 1990-03-20" in ctx
+    assert "Sex at birth: female" in ctx