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/analytics/test_api.py

@@ -0,0 +1,149 @@
+"""Unit tests for app.analytics.api."""
+
+from __future__ import annotations
+
+from unittest.mock import AsyncMock, MagicMock, patch
+
+import pytest
+from fastapi import FastAPI
+from fastapi.testclient import TestClient
+
+pytestmark = pytest.mark.unit
+
+
+def _build_app() -> FastAPI:
+    from app.analytics.api import router
+
+    app = FastAPI()
+    app.include_router(router)
+    return app
+
+
+def _make_mock_pool() -> MagicMock:
+    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
+    return mock_pool
+
+
+def _make_analytics_result() -> object:
+    from app.analytics.models import AgentUsage, AnalyticsResult, InterruptStats
+
+    return AnalyticsResult(
+        range="7d",
+        total_conversations=50,
+        resolution_rate=0.8,
+        escalation_rate=0.1,
+        avg_turns_per_conversation=3.5,
+        avg_cost_per_conversation_usd=0.02,
+        agent_usage=(AgentUsage(agent="order_agent", count=30, percentage=60.0),),
+        interrupt_stats=InterruptStats(total=5, approved=4, rejected=1, expired=0),
+    )
+
+
+def _get_analytics(app: FastAPI, path: str = "/api/analytics", **patch_kwargs: object) -> object:
+    """Helper: patch get_analytics, make request, return (response, mock)."""
+    analytics_result = _make_analytics_result()
+    with (
+        patch("app.analytics.api.get_analytics", return_value=analytics_result) as mock_ga,
+        TestClient(app) as client,
+    ):
+        resp = client.get(path)
+    return resp, mock_ga
+
+
+class TestAnalyticsEndpoint:
+    def test_returns_200_with_default_range(self) -> None:
+        app = _build_app()
+        app.state.pool = _make_mock_pool()
+        resp, _ = _get_analytics(app)
+
+        assert resp.status_code == 200
+        body = resp.json()
+        assert body["success"] is True
+        assert body["error"] is None
+        assert body["data"]["range"] == "7d"
+
+    def test_returns_correct_analytics_structure(self) -> None:
+        app = _build_app()
+        app.state.pool = _make_mock_pool()
+        resp, _ = _get_analytics(app)
+
+        data = resp.json()["data"]
+        assert "total_conversations" in data
+        assert "resolution_rate" in data
+        assert "escalation_rate" in data
+        assert "avg_turns_per_conversation" in data
+        assert "avg_cost_per_conversation_usd" in data
+        assert "agent_usage" in data
+        assert "interrupt_stats" in data
+
+    def test_custom_range_7d(self) -> None:
+        app = _build_app()
+        app.state.pool = _make_mock_pool()
+        resp, mock_ga = _get_analytics(app, "/api/analytics?range=7d")
+
+        assert resp.status_code == 200
+        mock_ga.assert_called_once()
+        call_kwargs = mock_ga.call_args
+        assert call_kwargs[1]["range_days"] == 7 or call_kwargs[0][1] == 7
+
+    def test_custom_range_30d(self) -> None:
+        app = _build_app()
+        app.state.pool = _make_mock_pool()
+        resp, mock_ga = _get_analytics(app, "/api/analytics?range=30d")
+
+        assert resp.status_code == 200
+        call_kwargs = mock_ga.call_args
+        assert call_kwargs[1].get("range_days") == 30 or (
+            len(call_kwargs[0]) > 1 and call_kwargs[0][1] == 30
+        )
+
+    def test_invalid_range_format_returns_400(self) -> None:
+        app = _build_app()
+        app.state.pool = _make_mock_pool()
+
+        with TestClient(app) as client:
+            resp = client.get("/api/analytics?range=invalid")
+
+        assert resp.status_code == 400
+
+    def test_range_without_d_suffix_returns_400(self) -> None:
+        app = _build_app()
+        app.state.pool = _make_mock_pool()
+
+        with TestClient(app) as client:
+            resp = client.get("/api/analytics?range=7")
+
+        assert resp.status_code == 400
+
+    def test_agent_usage_in_response(self) -> None:
+        app = _build_app()
+        app.state.pool = _make_mock_pool()
+        resp, _ = _get_analytics(app)
+
+        data = resp.json()["data"]
+        assert len(data["agent_usage"]) == 1
+        assert data["agent_usage"][0]["agent"] == "order_agent"
+
+    def test_interrupt_stats_in_response(self) -> None:
+        app = _build_app()
+        app.state.pool = _make_mock_pool()
+        resp, _ = _get_analytics(app)
+
+        data = resp.json()["data"]
+        assert data["interrupt_stats"]["total"] == 5
+        assert data["interrupt_stats"]["approved"] == 4
+
+    def test_envelope_format(self) -> None:
+        app = _build_app()
+        app.state.pool = _make_mock_pool()
+        resp, _ = _get_analytics(app)
+
+        body = resp.json()
+        assert "success" in body
+        assert "data" in body
+        assert "error" in body