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.

migrations/versions/a1b2c3d4e5f6_v2_app_settings.py

@@ -0,0 +1,32 @@
+"""V2 app_settings
+
+Revision ID: a1b2c3d4e5f6
+Revises: 57af90893f55
+Create Date: 2026-06-01 14:00:00.000000
+
+"""
+from typing import Sequence, Union
+
+from alembic import op
+import sqlalchemy as sa
+
+
+# revision identifiers, used by Alembic.
+revision: str = 'a1b2c3d4e5f6'
+down_revision: Union[str, Sequence[str], None] = '57af90893f55'
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    """Upgrade schema."""
+    op.create_table('app_settings',
+    sa.Column('key', sa.Text(), nullable=False),
+    sa.Column('value', sa.Text(), nullable=True),
+    sa.PrimaryKeyConstraint('key')
+    )
+
+
+def downgrade() -> None:
+    """Downgrade schema."""
+    op.drop_table('app_settings')