feat: complete phase 4 -- conversation replay API + analytics dashboard

- Replay models: StepType enum, ReplayStep, ReplayPage frozen dataclasses
- Checkpoint transformer: PostgresSaver JSONB -> structured timeline steps
- Replay API: GET /api/conversations (paginated), GET /api/replay/{thread_id}
- Analytics models: AgentUsage, InterruptStats, AnalyticsResult
- Analytics event recorder: Protocol + PostgresAnalyticsRecorder + NoOp
- Analytics queries: resolution_rate, agent_usage, escalation_rate, cost, interrupts
- Analytics API: GET /api/analytics?range=Xd with envelope response
- DB migration: analytics_events table + conversations column additions
- 74 new tests, 399 total passing, 92.87% coverage

backend/tests/unit/test_db_phase4.py

@@ -0,0 +1,55 @@
+"""Phase 4 DB migration tests -- analytics_events table and conversation columns."""
+
+from __future__ import annotations
+
+from unittest.mock import AsyncMock, MagicMock
+
+import pytest
+
+pytestmark = pytest.mark.unit
+
+
+class TestAnalyticsEventsDDL:
+    def test_analytics_events_ddl_exists(self) -> None:
+        from app.db import _ANALYTICS_EVENTS_DDL
+
+        assert "CREATE TABLE IF NOT EXISTS analytics_events" in _ANALYTICS_EVENTS_DDL
+
+    def test_analytics_events_ddl_has_required_columns(self) -> None:
+        from app.db import _ANALYTICS_EVENTS_DDL
+
+        assert "thread_id" in _ANALYTICS_EVENTS_DDL
+        assert "event_type" in _ANALYTICS_EVENTS_DDL
+        assert "agent_name" in _ANALYTICS_EVENTS_DDL
+        assert "tool_name" in _ANALYTICS_EVENTS_DDL
+        assert "tokens_used" in _ANALYTICS_EVENTS_DDL
+        assert "cost_usd" in _ANALYTICS_EVENTS_DDL
+        assert "duration_ms" in _ANALYTICS_EVENTS_DDL
+        assert "success" in _ANALYTICS_EVENTS_DDL
+        assert "error_message" in _ANALYTICS_EVENTS_DDL
+        assert "metadata" in _ANALYTICS_EVENTS_DDL
+
+    def test_conversations_migration_ddl_exists(self) -> None:
+        from app.db import _CONVERSATIONS_MIGRATION_DDL
+
+        assert "ALTER TABLE" in _CONVERSATIONS_MIGRATION_DDL
+        assert "resolution_type" in _CONVERSATIONS_MIGRATION_DDL
+        assert "agents_used" in _CONVERSATIONS_MIGRATION_DDL
+        assert "turn_count" in _CONVERSATIONS_MIGRATION_DDL
+        assert "ended_at" in _CONVERSATIONS_MIGRATION_DDL
+        assert "IF NOT EXISTS" in _CONVERSATIONS_MIGRATION_DDL
+
+    @pytest.mark.asyncio
+    async def test_setup_app_tables_executes_analytics_ddl(self) -> None:
+        mock_conn = AsyncMock()
+        mock_ctx = AsyncMock()
+        mock_ctx.__aenter__ = AsyncMock(return_value=mock_conn)
+        mock_ctx.__aexit__ = AsyncMock(return_value=None)
+        mock_pool = MagicMock()
+        mock_pool.connection.return_value = mock_ctx
+
+        from app.db import setup_app_tables
+
+        await setup_app_tables(mock_pool)
+        # Now expects 4 statements: conversations, interrupts, analytics_events, migrations
+        assert mock_conn.execute.await_count == 4