feat: replace DuckDuckGo web search with Exa/Parallel MCP providers

[andyzengmath]

Problem

DuckDuckGo Lite web search has become unreliable. DDG now aggressively detects and blocks automated requests with CAPTCHAs, causing web search to silently return empty results. The proxy logs show:

⚠ DDG Lite returned CAPTCHA
⚠ All search providers failed

This affects all users who don't have a Brave API key configured, since DDG Lite was the default (and only free) provider.

Solution

Replace DuckDuckGo with Exa and Parallel MCP endpoints as the primary search backend — the same approach used by OpenCode (184k stars).

These providers:

• Use the standard JSON-RPC 2.0 MCP protocol (tools/call method)
• Work without API keys out of the box
• Are purpose-built for AI agent search queries
• Have no CAPTCHA or bot detection issues

Provider Priority Chain

1. Brave Search API    (if BRAVE_API_KEY set — unchanged)
2. Exa / Parallel MCP  (NEW — free, no key, 50/50 split with cross-fallback)
3. DuckDuckGo Lite     (demoted to fallback — may hit CAPTCHAs)
4. DuckDuckGo Instant  (last resort — limited to knowledge graph)

How It Works

• Traffic is split 50/50 between Exa and Parallel based on a deterministic hash of the search query
• If one provider fails, it automatically tries the other before falling through to DDG
• 25-second timeout per MCP request
• Response parsing handles both Exa's plain-text format and Parallel's JSON format

New Environment Variables (all optional)

Variable	Description
WEBSEARCH_PROVIDER	Force exa or parallel (default: auto 50/50 split)
EXA_API_KEY	Optional API key for Exa
PARALLEL_API_KEY	Optional Bearer token for Parallel

Testing

Verified working with claude-sonnet-4.5 through the proxy:

🔍 Web search: "latest version of Node.js"
✓ Exa returned 3 results

No configuration needed — just restart the proxy and web search works immediately.