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_models.py

@@ -0,0 +1,106 @@
+"""Unit tests for app.analytics.models."""
+
+from __future__ import annotations
+
+import pytest
+
+pytestmark = pytest.mark.unit
+
+
+class TestAgentUsage:
+    def test_agent_usage_construction(self) -> None:
+        from app.analytics.models import AgentUsage
+
+        au = AgentUsage(agent="order_agent", count=10, percentage=50.0)
+        assert au.agent == "order_agent"
+        assert au.count == 10
+        assert au.percentage == 50.0
+
+    def test_agent_usage_is_frozen(self) -> None:
+        from app.analytics.models import AgentUsage
+
+        au = AgentUsage(agent="a", count=1, percentage=100.0)
+        with pytest.raises((AttributeError, TypeError)):
+            au.count = 2  # type: ignore[misc]
+
+
+class TestInterruptStats:
+    def test_interrupt_stats_defaults(self) -> None:
+        from app.analytics.models import InterruptStats
+
+        stats = InterruptStats()
+        assert stats.total == 0
+        assert stats.approved == 0
+        assert stats.rejected == 0
+        assert stats.expired == 0
+
+    def test_interrupt_stats_custom_values(self) -> None:
+        from app.analytics.models import InterruptStats
+
+        stats = InterruptStats(total=10, approved=7, rejected=2, expired=1)
+        assert stats.total == 10
+        assert stats.approved == 7
+        assert stats.rejected == 2
+        assert stats.expired == 1
+
+    def test_interrupt_stats_is_frozen(self) -> None:
+        from app.analytics.models import InterruptStats
+
+        stats = InterruptStats()
+        with pytest.raises((AttributeError, TypeError)):
+            stats.total = 5  # type: ignore[misc]
+
+
+class TestAnalyticsResult:
+    def test_analytics_result_construction(self) -> None:
+        from app.analytics.models import AgentUsage, AnalyticsResult, InterruptStats
+
+        result = AnalyticsResult(
+            range="7d",
+            total_conversations=100,
+            resolution_rate=0.85,
+            escalation_rate=0.05,
+            avg_turns_per_conversation=4.2,
+            avg_cost_per_conversation_usd=0.03,
+            agent_usage=(AgentUsage(agent="order_agent", count=60, percentage=60.0),),
+            interrupt_stats=InterruptStats(total=5, approved=4, rejected=1, expired=0),
+        )
+        assert result.range == "7d"
+        assert result.total_conversations == 100
+        assert result.resolution_rate == 0.85
+        assert result.escalation_rate == 0.05
+        assert result.avg_turns_per_conversation == 4.2
+        assert result.avg_cost_per_conversation_usd == 0.03
+        assert len(result.agent_usage) == 1
+        assert result.interrupt_stats.total == 5
+
+    def test_analytics_result_is_frozen(self) -> None:
+        from app.analytics.models import AnalyticsResult, InterruptStats
+
+        result = AnalyticsResult(
+            range="7d",
+            total_conversations=0,
+            resolution_rate=0.0,
+            escalation_rate=0.0,
+            avg_turns_per_conversation=0.0,
+            avg_cost_per_conversation_usd=0.0,
+            agent_usage=(),
+            interrupt_stats=InterruptStats(),
+        )
+        with pytest.raises((AttributeError, TypeError)):
+            result.range = "30d"  # type: ignore[misc]
+
+    def test_analytics_result_empty_agent_usage(self) -> None:
+        from app.analytics.models import AnalyticsResult, InterruptStats
+
+        result = AnalyticsResult(
+            range="7d",
+            total_conversations=0,
+            resolution_rate=0.0,
+            escalation_rate=0.0,
+            avg_turns_per_conversation=0.0,
+            avg_cost_per_conversation_usd=0.0,
+            agent_usage=(),
+            interrupt_stats=InterruptStats(),
+        )
+        assert result.agent_usage == ()