feat: Issue backlog manager for triage automation (#1459)

Automated issue triage: categorize, find stale, estimate burn time,
generate markdown/JSON reports. Addresses timmy-home backlog (was 220,
now 148 open issues).

Closes #1459.

tests/test_issue_backlog_manager.py

@@ -0,0 +1,123 @@
+"""Tests for issue backlog manager."""
+
+import json
+from datetime import datetime, timezone, timedelta
+from unittest.mock import patch, MagicMock
+
+import pytest
+import sys
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).parent.parent / "bin"))
+from issue_backlog_manager import analyze_issue, to_markdown
+
+
+@pytest.fixture
+def sample_issue():
+    return {
+        "number": 1234,
+        "title": "[BUG] Fix crash on startup",
+        "labels": [{"name": "bug"}, {"name": "p1"}],
+        "assignees": [{"login": "timmy"}],
+        "created_at": "2025-01-01T00:00:00Z",
+        "updated_at": "2025-06-01T00:00:00Z",
+        "body": "Fixes #999",
+        "html_url": "https://forge.example.com/...",
+    }
+
+
+class TestAnalyzeIssue:
+    def test_categorizes_bug(self, sample_issue):
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["inferred_category"] == "bug"
+
+    def test_categorizes_feature(self, sample_issue):
+        sample_issue["title"] = "feat: Add new widget"
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["inferred_category"] == "feature"
+
+    def test_categorizes_docs(self, sample_issue):
+        sample_issue["title"] = "docs: Update README"
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["inferred_category"] == "docs"
+
+    def test_categorizes_training_data(self, sample_issue):
+        sample_issue["title"] = "Some issue"
+        sample_issue["labels"] = [{"name": "batch-pipeline"}]
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["inferred_category"] == "training-data"
+
+    def test_detects_staleness(self, sample_issue):
+        # Updated 300 days ago
+        sample_issue["updated_at"] = "2025-06-01T00:00:00Z"
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["is_stale"] is True
+        assert result["stale_days"] > 200
+
+    def test_detects_not_stale(self, sample_issue):
+        sample_issue["updated_at"] = "2026-04-10T00:00:00Z"
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["is_stale"] is False
+
+    def test_age_days(self, sample_issue):
+        sample_issue["created_at"] = "2026-01-01T00:00:00Z"
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["age_days"] > 100
+
+    def test_has_assignee(self, sample_issue):
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["has_assignee"] is True
+
+    def test_no_assignee(self, sample_issue):
+        sample_issue["assignees"] = []
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["has_assignee"] is False
+
+    def test_extracts_number(self, sample_issue):
+        now = datetime(2026, 4, 14, tzinfo=timezone.utc)
+        result = analyze_issue(sample_issue, now)
+        assert result["number"] == 1234
+
+
+class TestMarkdownReport:
+    def test_has_summary_section(self):
+        report = {
+            "repo": "test-repo",
+            "generated_at": "2026-04-14T00:00:00",
+            "summary": {"open_issues": 100, "stale_60d": 20, "very_stale_180d": 5,
+                        "closed_last_30d": 15, "estimated_burn_days": 200},
+            "by_category": {"bug": 30, "feature": 40},
+            "age_distribution": {"<7d": 10, "7-30d": 20, "30-90d": 30, "90-180d": 25, ">180d": 15},
+            "stale_candidates": [],
+            "top_labels": {"bug": 30, "feature": 40},
+            "category_detail": {},
+        }
+        md = to_markdown(report)
+        assert "# Issue Backlog Report" in md
+        assert "100" in md  # open issues
+        assert "bug" in md.lower()
+
+    def test_shows_stale_candidates(self):
+        report = {
+            "repo": "test",
+            "generated_at": "2026-04-14",
+            "summary": {"open_issues": 1, "stale_60d": 1, "very_stale_180d": 1,
+                        "closed_last_30d": 0, "estimated_burn_days": 999},
+            "by_category": {},
+            "age_distribution": {},
+            "stale_candidates": [{"number": 99, "title": "Old issue", "stale_days": 500}],
+            "top_labels": {},
+            "category_detail": {},
+        }
+        md = to_markdown(report)
+        assert "#99" in md
+        assert "500" in md