Evaluate Claude Code SDK as an alternative backend

## Idea

The Claude Code SDK could potentially replace the current custom OpenRouter-based proxy server as the chatbot backend. This would leverage Anthropic's built-in agentic infrastructure rather than the current homebrewed approach.

## Pros

- Built-in task decomposition, checklists, and structured multi-step execution
- Self-verification loops that could improve reliability for complex operations (e.g., large author list imports)
- Better handling of large context through automatic task breakdown
- Active development with rapid improvements from Anthropic
- Could use Haiku as the base model to keep costs low

## Cons

- Ties the project more closely to Anthropic/Claude (currently model-agnostic via OpenRouter)
- May require significant refactoring of the current architecture
- Would need to evaluate cost implications (current free tier uses Jeremy's server with API keys)
- SDK capabilities and API may change rapidly
- Less control over the underlying behavior compared to custom implementation

## Context

From discussion with @satra on 2025-03-05. Worth evaluating as the project matures.

No files, tests, or entry points are named. Start by mapping the current custom OpenRouter-based proxy server and then compare it with the Claude Code SDK, including agentic capabilities, architecture changes, API stability, and cost; done means a documented evaluation and a clear recommendation.

Written by the indexing model from the issue text.