Remove github-proxy and all references from the docs and from any deploy-sourcegraph* repo.

• Remove mentions of GITHUB_BASE_URL everywhere
• Implement redsync based locking in github clients: https://github.com/sourcegraph/sourcegraph/pull/56485
• Remove github-proxy code: https://github.com/sourcegraph/sourcegraph/pull/56485
• Remove github-proxy from deployments:
  • Cloud controller
  • Remove GitHub proxy service deploy-sourcegraph#4268
  • Remove GitHub proxy service deploy-sourcegraph-docker#942
  • Remove GitHub proxy service deploy-sourcegraph-k8s#49
  • Remove GitHub proxy service deploy-sourcegraph-helm#348
  • Remove GitHub proxy service deploy-sourcegraph-docker-customer-replica-1#49
  • Any other repos?
  • Add to main repo changelog
  • Add upgrade notice to 5.3: https://github.com/sourcegraph/sourcegraph/blob/main/doc/admin/updates/kubernetes.md
• github-proxy set the IdleConnTimeout to 30s, stating the following:

  // Use a custom client/transport because GitHub closes keep-alive
  // connections after 60s. In order to avoid running into EOF errors, we use
  // a IdleConnTimeout of 30s, so connections are only kept around for <30s
  

• We sometimes see ErrTaken errors in S2
• Consider tuning back the logger.Error statements to logger.Warn

/cc @sourcegraph/source