feat(git-ops): add GitHub provider with auto-detection

Implements GitHub API provider following the same pattern as Gitea:
- Full PR operations (create, get, list, merge, update, close)
- Branch operations via API
- Comment and label management
- Reviewer request support
- Rate limit error handling

Server enhancements:
- Auto-detect provider from repository URL (github.com vs custom Gitea)
- Initialize GitHub provider when token is configured
- Health check includes both provider statuses
- Token selection based on repo URL for clone/push operations

Refs: #110

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

mcp-servers/git-ops/providers/__init__.py

@@ -6,5 +6,6 @@ Provides adapters for different git hosting platforms (Gitea, GitHub, GitLab).
 
 from .base import BaseProvider
 from .gitea import GiteaProvider
+from .github import GitHubProvider
 
-__all__ = ["BaseProvider", "GiteaProvider"]
+__all__ = ["BaseProvider", "GiteaProvider", "GitHubProvider"]