feat: Add PR backlog management process (#1470)

## Summary
Added tools and process for managing PR backlog in timmy-config.

## Problem
timmy-config has 31+ open PRs, the highest in the organization.
This creates confusion, slows down development, and increases
merge conflicts.

## Solution
Created automated tools and process for PR backlog management:

### 1. PR Backlog Analyzer (`scripts/pr-backlog-analyzer.py`)
- Fetches all open PRs from timmy-config
- Analyzes age, review status, labels
- Generates markdown report
- Categorizes PRs: stale, needs review, approved, changes requested

### 2. GitHub Actions Workflow (`.github/workflows/pr-backlog-management.yml`)
- Runs weekly on Monday at 10 AM UTC
- Analyzes PR backlog
- Creates issue if backlog is high (>10 stale PRs)
- Uploads report as artifact

### 3. Documentation (`docs/pr-backlog-process.md`)
- Weekly analysis process
- Review stale PRs procedure
- Merge approved PRs workflow
- Review pending PRs SLA
- Close duplicate PRs process
- Metrics to track
- Escalation procedures

## Usage

### Run Analyzer
```bash
python scripts/pr-backlog-analyzer.py
```

### View Report
```bash
cat reports/pr-backlog-$(date +%Y%m%d).md
```

## Metrics
- **Current**: 32 open PRs in timmy-config
- **Target**: <20 open PRs
- **SLA**: Review within 48 hours, merge within 7 days

Issue: #1470

docs/pr-backlog-process.md

@@ -0,0 +1,126 @@
+# PR Backlog Management Process
+
+## Overview
+
+This document outlines the process for managing PR backlog in the Timmy Foundation repositories, specifically addressing the high PR backlog in timmy-config.
+
+## Current State
+
+As of the latest analysis:
+- **timmy-config**: 31 open PRs (highest in org)
+- **the-nexus**: Multiple PRs for same issues
+- **hermes-agent**: Moderate PR count
+
+## Process
+
+### 1. Weekly Analysis
+
+Run the PR backlog analyzer weekly:
+
+```bash
+python scripts/pr-backlog-analyzer.py
+```
+
+This generates a report in `reports/pr-backlog-YYYYMMDD.md`.
+
+### 2. Review Stale PRs
+
+PRs older than 30 days are considered stale. For each stale PR:
+
+1. **Check relevance**: Is the PR still needed?
+2. **Check conflicts**: Does it conflict with current main?
+3. **Check activity**: Has there been recent activity?
+4. **Action**: Close, update, or merge
+
+### 3. Merge Approved PRs
+
+PRs with approvals should be merged within 7 days:
+
+1. **Verify CI**: Ensure all checks pass
+2. **Verify review**: At least 1 approval
+3. **Merge**: Use squash merge for clean history
+4. **Delete branch**: Clean up after merge
+
+### 4. Review Pending PRs
+
+PRs waiting for review should be reviewed within 48 hours:
+
+1. **Assign reviewer**: Ensure someone is responsible
+2. **Review**: Check code quality, tests, documentation
+3. **Approve or request changes**: Don't leave PRs in limbo
+4. **Follow up**: If no response in 48 hours, escalate
+
+### 5. Close Duplicate PRs
+
+Multiple PRs for the same issue should be consolidated:
+
+1. **Identify duplicates**: Same issue number or similar changes
+2. **Keep newest**: Usually the most up-to-date
+3. **Close older**: With explanatory comments
+4. **Document**: Update issue with which PR was kept
+
+## Automation
+
+### GitHub Actions Workflow
+
+The `pr-backlog-management.yml` workflow runs weekly to:
+
+1. Analyze all open PRs
+2. Generate a report
+3. Create an issue if backlog is high (>10 stale PRs)
+
+### Manual Trigger
+
+The workflow can be triggered manually via GitHub Actions UI.
+
+## Metrics
+
+Track these metrics weekly:
+
+- **Total open PRs**: Should be <20 per repo
+- **Stale PRs**: Should be <5 per repo
+- **Average PR age**: Should be <14 days
+- **Time to review**: Should be <48 hours
+- **Time to merge**: Should be <7 days after approval
+
+## Escalation
+
+If backlog exceeds thresholds:
+
+1. **Level 1**: Automated issue created
+2. **Level 2**: Team lead notified
+3. **Level 3**: Organization-wide cleanup sprint
+
+## Tools
+
+### PR Backlog Analyzer
+
+```bash
+# Run analysis
+python scripts/pr-backlog-analyzer.py
+
+# View report
+cat reports/pr-backlog-$(date +%Y%m%d).md
+```
+
+### Manual Cleanup
+
+```bash
+# List stale PRs
+curl -s -H "Authorization: token $GITEA_TOKEN"   "https://forge.alexanderwhitestone.com/api/v1/repos/Timmy_Foundation/timmy-config/pulls?state=open" |   jq -r '.[] | select(.created_at < "'$(date -u -d '30 days ago' +%Y-%m-%dT%H:%M:%SZ)'") | .number'
+
+# Close a PR
+curl -s -X PATCH -H "Authorization: token $GITEA_TOKEN"   -H "Content-Type: application/json"   -d '{"state": "closed"}'   "https://forge.alexanderwhitestone.com/api/v1/repos/Timmy_Foundation/timmy-config/pulls/123"
+```
+
+## Success Criteria
+
+- **Short-term**: Reduce timmy-config PRs from 31 to <20
+- **Medium-term**: Maintain <15 open PRs across all repos
+- **Long-term**: Automated PR lifecycle management
+
+## Related
+
+- Issue #1470: process: Address timmy-config PR backlog (9 PRs - highest in org)
+- Issue #1127: Evening triage pass
+- Issue #1128: Forge Cleanup