Add LLM settings integration

Add app_settings migration, settings UI, and OpenAI-compatible httpx LLM client with mocked tests.

Preserve API keys on blank form submissions, require a fresh key when base_url changes, and keep AI search settings untouched for step 3.

Update docs/design LLM integration and step 3 AI search notes, including prompt contract and extra-hints planning.

app/models.py

@@ -90,3 +90,10 @@ class SubItem(Base):
     )
 
     parent_item: Mapped[Item] = relationship(back_populates="subitems")
+
+
+class AppSetting(Base):
+    __tablename__ = "app_settings"
+
+    key: Mapped[str] = mapped_column(Text, primary_key=True)
+    value: Mapped[str | None] = mapped_column(Text, nullable=True)