### Backlog Health & Stale Policy Optimization

#### Problem Statement
Current repository metrics (`latency`, `throughput`) suffer from **survivorship bias**: they only sample the last 100 *closed* items, making the repository appear healthier than it is. Meanwhile, a stable backlog of **2342 open issues** and **442 open PRs** persists, largely due to "staleness immunity" for `help wanted` items and throttling in the standard stale workflow.

#### Changes
1.  **New Metric: Backlog Age**: Added `tools/gemini-cli-bot/metrics/scripts/backlog_age.ts` to measure the median age of the oldest 100 open issues and PRs. This exposes the "Slow Path" bottleneck that was previously invisible.
2.  **Stale Policy Throttling Fix**: Increased `operations-per-run` from 30 (default) to 200 in `.github/workflows/stale.yml` to allow the daily cron to actually make progress on the large backlog.
3.  **Help-Wanted Expiration**: Updated `gemini-scheduled-stale-issue-closer.yml` to remove the infinite exemption for `help wanted` issues. They are now eligible for stale closure if they are older than 180 days and have no recent human activity.

#### Expected Impact
- **Visibility**: The new `backlog_age` metrics will likely show high values initially, providing a baseline for backlog reduction efforts.
- **Efficiency**: Throttling fix will increase the rate of stale item closure.
- **Backlog Reduction**: The 6-month expiration for `help wanted` will finally address legacy "immortal" issues that have been bloating the backlog for years.

This is a surgical PR focused on repository health and metric accuracy.

tools/gemini-cli-bot/metrics/scripts/backlog_age.ts

@@ -0,0 +1,64 @@
+/**
+ * @license
+ * Copyright 2026 Google LLC
+ * SPDX-License-Identifier: Apache-2.0
+ */
+
+import { execSync } from 'node:child_process';
+import { GITHUB_OWNER, GITHUB_REPO } from '../types.js';
+
+try {
+  const query = `
+  query($owner: String!, $repo: String!) {
+    repository(owner: $owner, name: $repo) {
+      issues(states: OPEN, first: 100, orderBy: {field: CREATED_AT, direction: ASC}) {
+        totalCount
+        nodes {
+          createdAt
+        }
+      }
+      pullRequests(states: OPEN, first: 100, orderBy: {field: CREATED_AT, direction: ASC}) {
+        totalCount
+        nodes {
+          createdAt
+        }
+      }
+    }
+  }
+  `;
+  const output = execSync(
+    `gh api graphql -F owner=${GITHUB_OWNER} -F repo=${GITHUB_REPO} -f query='${query}'`,
+    { encoding: 'utf-8', stdio: ['ignore', 'pipe', 'ignore'] },
+  ).trim();
+  const parsed = JSON.parse(output);
+  const data = parsed?.data?.repository;
+
+  if (data?.issues?.totalCount > 100) {
+    process.stderr.write(`Warning: Backlog has ${data.issues.totalCount} issues, but only the oldest 100 were used for median calculation.\n`);
+  }
+  if (data?.pullRequests?.totalCount > 100) {
+    process.stderr.write(`Warning: Backlog has ${data.pullRequests.totalCount} PRs, but only the oldest 100 were used for median calculation.\n`);
+  }
+
+  const calculateMedianAgeDays = (nodes: { createdAt: string }[]) => {
+    if (!nodes || nodes.length === 0) return 0;
+    const now = Date.now();
+    const ages = nodes.map(
+      (n) => (now - new Date(n.createdAt).getTime()) / (1000 * 60 * 60 * 24),
+    );
+    ages.sort((a, b) => a - b);
+    const mid = Math.floor(ages.length / 2);
+    return ages.length % 2 !== 0
+      ? ages[mid]
+      : (ages[mid - 1] + ages[mid]) / 2;
+  };
+
+  const issueAge = calculateMedianAgeDays(data?.issues?.nodes ?? []);
+  const prAge = calculateMedianAgeDays(data?.pullRequests?.nodes ?? []);
+
+  process.stdout.write(`backlog_age_issue_median_days,${Math.round(issueAge * 100) / 100}\n`);
+  process.stdout.write(`backlog_age_pr_median_days,${Math.round(prAge * 100) / 100}\n`);
+} catch (err) {
+  process.stderr.write(err instanceof Error ? err.message : String(err));
+  process.exit(1);
+}