feat: add GitHub Copilot as LLM backend

[btotharye]

Description

• Create CopilotBackend class routing to api.githubcopilot.com/v1
• Support GitHub token authentication (env var or CLI option)
• Full streaming and non-streaming support
• Integrate with analyzer.py and CLI
• Comprehensive tests (28 tests, 89% coverage)
• Update documentation and backends guide
• All ruff and mypy checks pass

Type of Change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Documentation update
• Content pack addition/update
• CI/CD or tooling change

Changes Made

Testing

• Tests pass locally (make test)
• Linting passes (make lint)
• Formatting is correct (make format-check)
• Tested manually with:

Related Issues

Checklist

• My code follows the project's style guidelines
• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings or errors
• I have added tests that prove my fix is effective or that my feature works
• New and existing tests pass locally with my changes

Additional Notes

[codecov]

Codecov Report

❌ Patch coverage is 93.33333% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 94.51%. Comparing base (3fbd8b5) to head (9070c55).

Files with missing lines	Patch %	Lines
greybeard/cli.py	76.92%	3 Missing ⚠️
greybeard/analyzer.py	95.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #60      +/-   ##
==========================================
+ Coverage   94.41%   94.51%   +0.09%     
==========================================
  Files          33       34       +1     
  Lines        3655     3701      +46     
==========================================
+ Hits         3451     3498      +47     
+ Misses        204      203       -1     

Flag	Coverage Δ
unittests	94.51% <93.33%> (+0.09%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.