feature: Implement Anthropic external provider (Phase 2)

[shernshiou]

Describe the feature

Add support for Anthropic as an external provider, enabling the integration of Anthropic's APIs into the production-stack. This should allow users to select and use Anthropic alongside other providers.\n\nSuggested steps:

• Create AnthropicProvider by referencing OpenAIProvider (see src/vllm_router/external_providers/openai_provider.py) and inherit from ExternalProviderAdapter (base.py).
• Implement essential methods: send_request, health_check, fetch_available_model_ids, and close in the adapter.
• Register 'anthropic' in the provider registry (see src/vllm_router/external_providers/registry.py).
• Add Anthropic example entry to the YAML config schema (see examples in the RFC or the OpenAI provider).
• Add or update tests in [src/tests/external_providers/].

Why do you need this feature?

Supporting Anthropic will expand provider compatibility, allowing users to leverage Anthropic models for various use cases and giving more flexibility when deploying LLM solutions.

Additional context

This is a follow-up to #883, which introduced the external provider architecture and OpenAI integration. Please review the design and RFC described in #883 for context and adapt the architecture patterns.

[shernshiou]

I will implement this feature.