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/app/db.py

@@ -34,6 +34,31 @@ CREATE TABLE IF NOT EXISTS active_interrupts (
 );
 """
 
+_ANALYTICS_EVENTS_DDL = """
+CREATE TABLE IF NOT EXISTS analytics_events (
+    id BIGSERIAL PRIMARY KEY,
+    thread_id TEXT NOT NULL,
+    event_type TEXT NOT NULL,
+    agent_name TEXT,
+    tool_name TEXT,
+    tokens_used INTEGER NOT NULL DEFAULT 0,
+    cost_usd DOUBLE PRECISION NOT NULL DEFAULT 0.0,
+    duration_ms INTEGER,
+    success BOOLEAN,
+    error_message TEXT,
+    metadata JSONB NOT NULL DEFAULT '{}',
+    created_at TIMESTAMPTZ NOT NULL DEFAULT NOW()
+);
+"""
+
+_CONVERSATIONS_MIGRATION_DDL = """
+ALTER TABLE conversations
+    ADD COLUMN IF NOT EXISTS resolution_type TEXT,
+    ADD COLUMN IF NOT EXISTS agents_used TEXT[],
+    ADD COLUMN IF NOT EXISTS turn_count INTEGER NOT NULL DEFAULT 0,
+    ADD COLUMN IF NOT EXISTS ended_at TIMESTAMPTZ;
+"""
+
 
 async def create_pool(settings: Settings) -> AsyncConnectionPool:
     """Create an async connection pool with the required psycopg settings."""
@@ -55,7 +80,9 @@ async def create_checkpointer(pool: AsyncConnectionPool) -> AsyncPostgresSaver:
 
 
 async def setup_app_tables(pool: AsyncConnectionPool) -> None:
-    """Create application-specific tables (conversations, active_interrupts)."""
+    """Create application-specific tables and apply migrations."""
     async with pool.connection() as conn:
         await conn.execute(_CONVERSATIONS_DDL)
         await conn.execute(_INTERRUPTS_DDL)
+        await conn.execute(_ANALYTICS_EVENTS_DDL)
+        await conn.execute(_CONVERSATIONS_MIGRATION_DDL)